RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals

Meta Title: RD Sharma Solutions for Class 12 Maths Chapter 19 – Indefinite Integrals – Get free PDF

Meta Description: RD Sharma Solutions for Class 12 Maths Chapter 19 – Indefinite Integrals comprises detailed solutions to all the exercises present in this chapter.

The solutions PDF is a major reference guide to help students score well in the Class 12 examination. By solving the exercise wise problems daily helps students improve their problem solving and logical thinking skills, which are important to obtain a better academic score. The main aim is to help students self analyse the areas, which require more practice from the exam perspective. With the help of RD Sharma Solutions, students can solve the exercise problems in a shorter duration with a clear idea of the concepts.

The 19th Chapter, Indefinite Integrals of RD Sharma Solutions for Class 12 Maths explains some standard results on integration along with fundamental integration formulae. The main aim of these solutions formulated by BYJU’S experts is to provide a fundamental aspect of Maths, which in turn, helps students to understand every concept clearly. Some of the essential topics covered in this chapter are listed below.

  • Definition of primitive or antiderivative
  • Definition and meaning of indefinite integral
  • Fundamental integration formulae
  • Some standard results on integration along with the corollary
  • Integration of trigonometric functions
  • Integration of exponential functions
  • Miscellaneous problems
  • Geometrical interpretation of indefinite integral
  • Comparison between differentiation and integration
  • Methods of integration
  • Integration by substitution
  • Some standard results
  • Evaluation of integrals by using trigonometric substitutions
  • Some special integrals
  • Integration by parts
  • Some important integrals along with theorems
  • Integration of rational algebraic functions by using partial fractions
    • When the denominator is expressible as a product of distinct linear factors
    • When denominator contains some repeating linear factors
    • The denominator contains irreducible quadratic factors
  • Integration of some special irrational algebraic functions

Download the PDF of RD Sharma Solutions For Class 12 Maths Chapter 19 Indefinite Integrals

 

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Access answers to Maths RD Sharma Solutions For Class 12 Chapter 19 – Indefinite Integrals

Exercise 19.1 Page No: 19.4

1. Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 1

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 2

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 3

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 4

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 5

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 6

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 7

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 8

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 9

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 10

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 11

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 12

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 13

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 14

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 15

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 16

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 17

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 18

2. Evaluate:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 19

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 20

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 21

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 22

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 23

3. Evaluate:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 24

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 25


Exercise 19.2 Page No: 19.14

Evaluate the following integrals (1 – 44):

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 26

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 27

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 28

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 29

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 30

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 30

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 31

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 32

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 33

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 34

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 35

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 36

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 37

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 38

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 39

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 40

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 41

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 42

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 43

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 44

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 45

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 46

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 47

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 48

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 49

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 50

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 51

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 52

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 53

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 54

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 55

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 56

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 57

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 58

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 59

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 60

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 61

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 62

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 63

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 64

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 65

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 66

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 67

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 68

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 69

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 70


Exercise 19.3 Page No: 19.23

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 71

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 72

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 73

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 74

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 75

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 76

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 77

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 78

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 79

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 80

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 81

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 82

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 83

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 84

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 85

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 86

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 87

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 88

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 89

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 90

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 91

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 93

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 94

Exercise 19.4 Page No: 19.30

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 95

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 96

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 97

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 98

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 99

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 100

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 101

Exercise 19.5 Page No: 19.33

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 102

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 103

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 104

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 105

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 106

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 107

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 108

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 109

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 110

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 111

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 112

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 113

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 114

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RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 116

Exercise 19.6 Page No: 19.36

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 118

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 119

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 120

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 121

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 122

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 123

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 124

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 125

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 126

Exercise 19.7 Page No: 19.38

Integrate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 127

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 128

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 129

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 130

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 131

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 132

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 133

Exercise 19.8 Page No: 19.47

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 134

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 135

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 136

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 137

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 138

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 139

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 140

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 141

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 142

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 143

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 144

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 145

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 147

Exercise 19.9 Page No: 19.57

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 148 dx

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 149

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 151

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RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 153

Solution:

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 157

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 159

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RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 161

Solution:

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Solution:

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Solution:

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Solution:

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RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 170

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 171

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Exercise 19.10 Page No: 19.65

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 174

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 176

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RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 179

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 180

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 181

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Solution:

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 185

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 186

Exercise 19.11 Page No: 19.69

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 187

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 188

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 189

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 190

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 191

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Solution:

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Solution:

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 199

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 200

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 201

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 202

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 203

Exercise 19.12 Page No: 19.73

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 204

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 205

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 206

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 207

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 208

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 209

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 210

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 211

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 212

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 213

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 214

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 215

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 216

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 217

Exercise 19.13 Page No: 19.79

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 218

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 219

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 220

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 221

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 222

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 223

Exercise 19.14 Page No: 19.83

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 224

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 225

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 226

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 227

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 228

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 229

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 230

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 231

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 232

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 233

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 234

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 235

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 236

Exercise 19.15 Page No: 19.86

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 237

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 238

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 239

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 240

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 241

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 242

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 243

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 244

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 245

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 246

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 247

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 248

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 249

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 250

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 251

Exercise 19.16 Page No: 19.90

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 252

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 253

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 254

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 255

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 256

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 257

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 258

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 259

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 260

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 261

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 262

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 263

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 264

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 265

Exercise 19.17 Page No: 19.93

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 266

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 267

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 268

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 269

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 270

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 271

C:\Users\tnluser\Downloads\CodeCogsEqn - 2020-01-30T120903.568.gif

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 273

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 274

C:\Users\tnluser\Downloads\CodeCogsEqn - 2020-01-30T121259.367.gif

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 276

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 277

Exercise 19.18 Page No: 19.98

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 278

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 279

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 280

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 281

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 282

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 283

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 284

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 285

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 286

Solution:

Let sin x = t

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 287

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 288

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 289

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 290

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 291

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 292

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 293

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 294

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 295

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 296

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 297

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 298

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 299

Exercise 19.19 Page No: 19.104

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 300

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 301

We will solve I1 and I2 individually.

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 302

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 303

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 304

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 305

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 306

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 307

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 308

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 309

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 310

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 311

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 312

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 313

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 314

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 315

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 316

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 317

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 318

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 319

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 320

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 321

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 322

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 323

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 324

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 325

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 326

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 327

Exercise 19.20 Page No: 19.106

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 328

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 329

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 330

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 331

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 332

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 333

⇒ 1 = (A + B) x + (3A – 2B)

⇒ Then A + B = 0 … (1)

And 3A – 2B = 1 … (2)

Solving (1) and (2),

2 × (1) → 2A + 2B = 0

1 × (2) → 3A – 2B = 1

5A = 1

∴ A = 1/5

Substituting A value in (1),

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 334

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 335

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 336

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 337

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 338

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 339

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 340

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 341

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 342

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 343

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 344

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 345

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 346

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 347

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 348

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 349

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 350

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 351

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 352

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 353

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 354

Exercise 19.21 Page No: 19.110

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 355

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 356

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 357

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 358

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 359

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 360

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 361

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 362

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 363

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 364

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 365

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 366

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 367

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 368

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 369

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 370

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 371

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 372

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 373

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 374

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 375

Exercise 19.22 Page No: 19.114

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 376

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 377

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 378

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 379

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 380

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 381

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 382

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 383

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 384

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 385

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 386

Exercise 19.23 Page No: 19.117

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 387

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 388

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 389

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 390

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 391

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 392

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 393

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 394

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 395

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 396

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 397

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 398

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 399

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 400

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 401

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 402

Exercise 19.24 Page No: 19.122

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 403

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 404

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 405

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 406

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 407

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 408

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 409

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 410

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 411

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 412

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 413

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 414

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 415

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 416

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 417

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 418

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 419

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 420

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 421

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 422

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 423

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 424

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 425

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 426

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 427

Exercise 19.25 Page No: 19.133

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 428

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 429

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 430

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 431

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 432

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 433

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 434

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 435

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 436

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 437

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 438

Exercise 19.26 Page No: 19.143

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 439

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 440

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 441

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 442

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 443

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 444

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 445

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 446

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 447

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 448

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 449

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 450

Exercise 19.27 Page No: 19.149

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 451

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 452

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 453

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 454

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 455

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 456

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 457

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 458

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 459

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 460

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 461

Exercise 19.28 Page No: 19.154

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 462

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 463

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 464

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 465

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 466

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 467

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 468

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 469

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 470

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 471

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 472

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 473

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 474

Exercise 19.29 Page No: 19.158

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 475

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 476

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 477

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 478

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 479

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 480

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 481

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 482

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 483

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 484

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 485

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 486

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 487

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 488

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 489

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 490

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 491

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 492

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 493

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 494

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 495

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 496

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 497

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 498

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 499

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 500

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 501

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 502

Exercise 19.30 Page No: 19.176

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 503

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 504

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 505

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 506

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 507

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 508

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 509

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 510

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 511

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 512

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 513

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 514

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 515

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 516

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 517

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 518

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 519

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 520

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 521

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 522

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 523

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 524

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 525

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 526

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 527

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 528

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 529

Exercise 19.31 Page No: 19.190

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 530

Solution:

The given equation can be written as,

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 531

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 532

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 533

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 534

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 535

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 536

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 537

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 538

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 539

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 540

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 541

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 542

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 543

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 544

Exercise 19.32 Page No: 19.196

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 545

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 546

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 547

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 548

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 549

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 550

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 551

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 552

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 553

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 554

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 555

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 556

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 557

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 558


Also, access RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals

Exercise 19.1 Solutions

Exercise 19.2 Solutions

Exercise 19.3 Solutions

Exercise 19.4 Solutions

Exercise 19.5 Solutions

Exercise 19.6 Solutions

Exercise 19.7 Solutions

Exercise 19.8 Solutions

Exercise 19.9 Solutions

Exercise 19.10 Solutions

Exercise 19.11 Solutions

Exercise 19.12 Solutions

Exercise 19.13 Solutions

Exercise 19.14 Solutions

Exercise 19.15 Solutions

Exercise 19.16 Solutions

Exercise 19.17 Solutions

Exercise 19.18 Solutions

Exercise 19.19 Solutions

Exercise 19.20 Solutions

Exercise 19.21 Solutions

Exercise 19.22 Solutions

Exercise 19.23 Solutions

Exercise 19.24 Solutions

Exercise 19.25 Solutions

Exercise 19.26 Solutions

Exercise 19.27 Solutions

Exercise 19.28 Solutions

Exercise 19.29 Solutions

Exercise 19.30 Solutions

Exercise 19.31 Solutions

Exercise 19.32 Solutions

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