NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals delivers the answers for all the questions of the chapter. Basics Maths are covered in the module to help students move ahead in their area of work. The NCERT syllabus ensures that the content included is apt for the students to move forward in their respective streams in the future. A student needs to understand the concept of Application Of Integrals as it is an important part of the question paper, while also the fundamentals of this chapter can be seen in higher grades. Before solving real-world applications and problems, the idea has to be learned thoroughly. This chapter will help the students to strengthen their foundation on the application of Integrals. Students can easily download and practice all the exercise-wise NCERT problems with solutions to score good marks in the final exams and get ready for any competitive exams. Download these NCERT Solutions of Class 12 maths and start practising offline.

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NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

The significant concepts of Class 12 Maths covered in Chapter 8 Application Of Integrals of NCERT Solutions include:

8.1 Introduction

This section contains recollecting the thoughts of finding areas bounded by the curve, definite integral as the limit of a sum, introduces the application of integrals such as the area under simple curves, between lines, parabolas and ellipses.

The average value of a function can be calculated using integration. 

The rainfall recorded during a day followed a curve R with specified limits. On integrating the given function from limit x to limit y, we obtain the average amount of rainfall of that particular day.

8.2 Area under simple curves

This section defines the area bounded by the curve y = f(x) using the formula. A few examples are discussed for your reference.

Imagine that you are sharing a round blanket with your sibling. If the two of you are accommodating, then the extent to which you will not be covered will depend on the size of the blanket. In mathematical terms, we define it as the area under the blanket available to the two of you.

These types of problems fall under the category of analysis of the area under curves. 

8.2.1 The area of the region bounded by a curve and a line

This section deals with finding the area of the space by a line and a circle, a line and a parabola, a line and an ellipse. The process of calculation is accompanied by a few illustrations.

8.3 Area between Two Curves

This section explains the method of finding the area between two curves with solved problems. 

It says that the area can be found by dividing the region into a number of pieces of small area and then adding up the area of those tiny pieces. It is easier to find the area if those tiny pieces are vertical in shape.

Exercise 8.1 Solutions : 13 Questions (8 Long, 3 Short, 2 MCQ)

Exercise 8.2 Solutions : 7 Questions(5 Long, 2 MCQ)

Miscellaneous Exercise Solutions: 19 Questions (8 Long, 7 Short, 4 MCQ)

In this chapter, students will deal with various Integrals applications. Some of the important concepts are listed below:

1. The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) is given by the formula: Area ab\int_{a}^{b} y dx = ab\int_{a}^{b}f(x) dx

2. The area of the region enclosed between two curves y = f (x), y = g (x) and the lines x = a, x = b is given by the formula,

Area = ab\int_{a}^{b} ; where f(x) ≥ g(x) in [a, b]

3. If f (x) ≥ g (x) in [a, c] and f (x) ≤ g (x) in [c, b], a < c < b, then

Area = ac\int_{a}^{c} + cb\int_{c}^{b}

NCERT Solutions For Class 12 Maths Chapter 8 Exercises:

Get detailed solution for all the questions listed under below exercises:

Exercise 8.1 Solutions : 13 Questions (8 Long, 3 Short, 2 MCQs)

Exercise 8.2 Solutions : 7 Questions(5 Long, 2 MCQs)

Miscellaneous Exercise Solutions: 19 Questions (8 Long, 7 Short, 4 MCQs)

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

The main topics covered NCERT Solutions for Class 12, Chapter 8-Application of Integrals are:

Exercise Topic
8.1 Introduction
8.2 Area under Simple Curves
8.3 Area between Two Curves.
Others Miscellaneous Q&A

Key Features of NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

  1. These NCERT Solutions are prepared with the help of subject experts.
  2. Help students to strengthen their basics on applications of Integrals.
  3. Well-structured content.
  4. All questions are solved with the help of diagrams.
  5. Help students in their assignments and competitive exams.

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