NCERT Solutions for Class 12 Maths Chapter 7- Integrals

NCERT Solutions For Class 12 Maths Chapter 7 PDF Free Download

The NCERT Solutions for Class 12 maths chapter 7, Integrals, is available here. The NCERT maths book of class 12 includes the concept of integrals in chapter 7. In this chapter, students learn about integral calculus (definite and indefinite), their properties and much more. This topic is extremely important for both CBSE board exam and for competitive exams.

The concepts of integrals are given in this chapter in a detailed and easy to understand manner. These class 12 NCERT solutions for integrals are very simple and can help the students in understanding the problem solving method very easily. Students can reach for these NCERT solutions and download it for free to practice them offline as well. These solved questions make the students understand the method of applying the concepts of Integrals in each problem.

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NCERT Solutions for Class 12 Maths Chapter 7- Integrals

The major concepts of Maths covered in the Chapter 7- Integrals of NCERT Solutions for Class 12 includes:

7.1 Introduction

7.2 Integration as an Inverse Process of Differentiation

7.2.1 Geometrical interpretation of indefinite integral

7.2.2 Some properties of indefinite integral

7.2.3 Comparison between differentiation and integration

7.3 Methods of Integration

7.3.1 Integration by substitution

7.3.2 Integration using trigonometric identities

7.4 Integrals of Some Particular Functions

7.5 Integration by Partial Fractions

7.6 Integration by Parts

7.7 Definite Integral

7.7.1 Definite integral as the limit of a sum

7.8 Fundamental Theorem of Calculus

7.8.1 Area function

7.8.2 First fundamental theorem of integral calculus

7.8.3 Second fundamental theorem of integral calculus

7.9 Evaluation of Definite Integrals by Substitution

7.10 Some Properties of Definite Integrals

Exercise 7.1 Solutions 22 Questions

Exercise 7.2 Solutions 39 Questions

Exercise 7.3 Solutions 24 Questions

Exercise 7.4 Solutions 25 Questions

Exercise 7.5 Solutions 23 Questions

Exercise 7.6 Solutions 24 Questions

Exercise 7.7 Solutions 11 Questions

Exercise 7.8 Solutions 6 Questions

Exercise 7.9 Solutions 22 Questions

Exercise 7.10 Solutions 10 Questions

Exercise 7.11 Solutions 21 Questions

Miscellaneous Exercise On Chapter 7 Solutions 44 Questions

NCERT Solutions for Class 12 Maths Chapter 7- Integrals

The chapter integrals belongs to the unit Calculus, that adds up to 35 marks of the total marks. There are 11 exercises along with a miscellaneous exercise in this chapter to help the students get thorough with the concept of Integrals. The Chapter 7 of NCERT Solutions for Class 12 Maths discusses the following:

  1. Integration is the inverse process of differentiation. In the differential calculus, we are given a function and we have to find the derivative or differential of this function, but in the integral calculus, we are to find a function whose differential is given. Thus, integration is a process which is the inverse of differentiation.
  2. From the geometric point of view, an indefinite integral is collection of family of curves, each of which is obtained by translating one of the curves parallel to itself upwards or downwards along the y-axis.
  3. Some properties of indefinite integrals.
  4. Some standard integrals
  5. Integration by partial fractions
  6. Integration by substitution: A change in the variable of integration often reduces an integral to one of the fundamental integrals. The method in which we change the variable to some other variable is called the method of substitution. When the integrand involves some trigonometric functions, we use some well known identities to find the integrals.
  7. Integration by parts: the integral of the product of two functions = first function × integral of the second function – integral of {differential coefficient of the first function × integral of the second function}.
  8. First fundamental theorem of integral calculus.
  9. Second fundamental theorem of integral calculus.

Key Features of NCERT Solutions for Class 12 Maths Chapter 7- Integrals

Learning the chapter Integrals enables the students to study the following:

Integration as the inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Key Features of NCERT Solutions for Class 12 Maths Chapter 7- Integrals

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.