# NCERT Solutions for Class 12 Maths Chapter 8 – Application of Integrals

Our NCERT Solutions for Class 12 Maths Chapter 8- Applications of Integrals have been carefully drafted by the best Maths teachers. This chapter comprises various important concepts that are important. Some of them are integrals used to find the area of a curved region, integrals used to find the area bounded by two curves, integrals used to find the area bounded by a curve and a line, and integrals used to find the area bounded by lines, between parabolas, between ellipses, between two lines, between a line and a parabola and between a line and an ellipse.

This chapter also throws light on the Walli formula and Leibnitz rule for differentiation under the integral sign. Our NCERT Solutions cover all concepts of this chapter in full details.

The CBSE NCERT Class 12 Maths Chapter 8 comprises 3 exercises with 13, 7 and 19 questions respectively. They adequately cover all topics of the chapter and give you enough practice to become thorough with the chapter. Our NCERT Solutions contain step by step solutions to all questions of all exercises in an easy to understand manner. Our NCERT Solutions help you learn from anywhere and anytime. They are just what you need to excel in your Class 12 board exams.

## NCERT Class 12 Maths Chapter 8: Important Topics

Our NCERT Solutions for Class 12 Maths Chapter 8 – Application of Integrals cover crucial concepts. Some of them have been discussed below.

**Integrals used to find the area of a curved region**

In this section of NCERT CBSE Class, 12 Maths Chapter 8 you will learn that integrals are functions that satisfy a given differential equation for finding the area of a curved region y=f(x), the x-axis and the line x=a and x=b(b>a) is denoted through the formula given below.

If the curved region is x=ϕ(y), y-axis and the line y=c, y=d then it is denoted through the formula given below.

**Integrals used to find the area bounded by two curves**

Here you will learn that if the dimensions of two curves are y=f(x), y=g(x) and lines x=a and x=b, then it is denoted by the formula given below.

**Leibnitz rule for Differentiation under the integral sign**

The Leibnitz rule gives a formula for differentiation of a definite integral, the limits of which are functions of the differential variable. The formula for the same has been represented below.

This chapter also discusses in details about how to use integrals to calculate the area bounded by a curve and a line, between two lines, between parabolas, ellipses, between a line and a circle, between a line and a parabola and between a line and an ellipse. It also explains explicitly about Walli’s formula.

### NCERT CBSE Class 12 Maths Chapter 8 Exercises

NCERT CBSE Class 12 Maths Chapter 8 consists of 2 exercises and 1 miscellaneous exercise. The exercises have been discussed below.

**Exercise 8.1**

This exercise consists of 13 questions. Out of these questions, 8 questions are long answer questions,3 are short answer questions, and 2 are MCQ. This exercise covers the topic area bounded by the curve, area surrounded by an ellipse, area bounded by a curve and a line, area of the region bounded by a parabola, area of a region bounded by a parabola and a vertical line. Our NCERT Solutions for Class 12 Maths Chapter 8 answer all questions of this exercise in a step by step manner to help you understand easily.

**Exercise 8.2**

This exercise consists of 7 questions. Out of these questions, 5 questions are long answer questions, and 2 questions are MCQs. Some of the topics covered in this exercise include the area of the circle which is in the interior of the parabola, area bounded by two curves, area of the region bounded by the triangle whose vertices are given, and area of the triangular region whose sides have the given equations.

**Miscellaneous Exercise**

This exercise comprises 19 questions. Out of these questions, 8 are long answer questions, 7 are short answer questions, and 4 are MCQs. This exercise covers all concepts from the chapter.

## Benefits of CBSE NCERT Class 12 Maths Chapter 8 Solutions

There are many upsides associated with learning, and practising problem sums from our well- structured and comprehensive NCERT Solutions for Class 12 Maths Chapter 8- Applications of Integrals. Some of them have been given below.

- Our NCERT Solutions are all-inclusive, exhaustive yet to the point.
- They are easy to understand and absolutely accurate
- They have been drafted by eminent Maths teaches on the bases of the latest guidelines given by CBSE and NCERT
- Our NCERT Solutions give a good amount of practice to clear all your doubts and become thorough with the chapter.
- They cover all corners of the chapter and cover a wide range of question types that are important from the Class 12 Board Exam perspective.
- They have been designed and developed in a manner to help you learn and revise quickly during your board exams.
- Our NCERT Solutions not only help you score high marks in your board exams but also score well in various competitive exams.