NCERT Solutions for Class 12 Maths, Chapter 7 - Integrals

In earlier chapters, you studied about Differentiation. In NCERT Solutions for Class 12 Maths, Chapter 7, you will study what integration is all about. In fact, integration is the inverse process of differentiation. In differentiation, you know what the function is, and you need to find the derivative of that function. However, in integration, you know the
derivative and need to find the function.

Isn’t that interesting? Integrals can be definite or indefinite. In this chapter, you’ll study
these integrals, their elementary properties and some useful techniques of integration.
Integration has wide applications in the fields of science, engineering, economics,
probability, finance and more.

Let’s take a look at topics and sub-topics of Class 12 Maths, Chapter 7 Integrals

7.1 Introduction
7.2 Integration as an Inverse Process of Differentiation
7.3 Methods of Integration
7.4 Integrals of some Particular Functions
7.5 Integration by Partial Fractions
7.6 Integration by Parts
7.7 Definite Integral
7.8 Fundamental Theorem of Calculus
7.9 Evaluation of Definite Integrals by Substitution
7.10 Some Properties of Definite Integrals

In Class 12 Maths Chapter 7, one will learn – 

Section 7.2 – In this section, you will learn about what integration is and make a
comparison between differentiation and integration.

Section 7.3 – In this section, you’ll study three important methods or techniques used
to find integrals. These methods are Integration by Substitution, Integration using
Partial Fractions and Integration by Parts.

Section 7.4 – In this section, you will acquire knowledge about some important
formulae of integrals and learn how to apply them for integrating many other related
standard integrals.

Section 7.5 – In this section, you’ll learn about partial fraction decomposition and how
to use it in integration in place of using proper rational functions.

Section 7.6 – In this section, you’ll study another important method of integration of
products of functions – Integration by parts.

Section 7.7 – In this section, you will learn what definite integral of a function is all
about. You will also come across terms like – ‘Integral as the limit of a sum’.

Section 7.8 – In this section, you’ll acquire knowledge about area function, first
the fundamental theorem of integral calculus and second the fundamental theorem of
integral calculus.

Section 7.9 – In this section, you’ll learn one more significant method for finding the
indefinite integral, i.e. the Method of Substitution.

Section 7.10 – This section reveals some important and useful properties (with their
proofs) of definite integrals, which help in assessing the definite integrals better.

To know more about the Class 12 Maths Chapter 7 Integrals, you should explore the
exercises below. You can also download the Integrals Class 12 NCERT Solutions PDF, solved by expert Maths trainers and also practice Class 12 Maths Chapter 7
Miscellaneous Exercise Solutions.