# NCERT Solutions for Class 12 Maths Chapter 7 Integrals

## NCERT Solutions for Class 12 Maths Chapter-7 Integrals

In this chapter we will learn about integral calculus ( both definite integral and indefinite integral), and also learn their properties and formulas. This topic is very important from the 12th CBSE board exam point of view and also important for competitive examinations like JEE Main and JEE Advance. Chapter 7 Integrals is the most important and most time-consuming chapter of class 12 mathematics because in this chapter there are 11 exercises with 227 questions and also 44 questions in a miscellaneous exercise. The NCERT Solutions for Class 12 Maths Chapter-7 Integrals are solved by maths experts for the students to develop a grip on the topic.

In this chapter, we will study the integrals of functions and its application like calculation of areas under the graphs. Integration is the inverse operation of differentiation. In the differential calculus, we are to find the differential or derivative of the given function, but in the integral calculus, differential of a function is given and our focus to find that function. Thus, integration is the inverse method of differentiation. In NCERT Class 12 Maths Chapter-7 Integrals we learn two integrals Definite integral and  Indefinite integral.

 Definite Integral Indefinite Integral Definition A definite Integral has upper and lower limits if  'a' and 'b' are the limits or boundaries. The definite integral of f(x) is a number, not function. An integral without upper limit and lower limit. It is also an antiderivative. The indefinite integral of f(x) is a function not number. Expression $\dpi{120} \int_{a}^{b}f(x)dx$ $F(x)=\int f(x)dx$

## 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

7.8.1Area 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

## NCERT Solutions for Class 12 Maths Chapter 7 Integrals- Exercise Questions

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.1

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.2

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.3

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.4

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.5

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.6

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.7

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.8

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.9

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.10

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise Miscellaneous

## NCERT Solutions for class 12- Maths

 Chapter 1 Relations and Functions Chapter 2 Inverse Trigonometric Functions Chapter 3 Matrices Chapter 4 Determinants Chapter 5 Continuity and Differentiability Chapter 6 Application of Derivatives Chapter 8 Application of Integrals Chapter 9 Differential Equations Chapter 10 Vector Algebra Chapter 11 Three Dimensional Geometry Chapter 12 Linear Programming Chapter 13 Probability