Integrals NCERT Solutions Class 12 introduces the concept of integrals as a reversal of differential and the mathematical approach to integrals. There is a preset bundle of functions for integrals of special equations which can be used to solve complex questions. The bundle has innumerable applications in several fields of study. Every subject uses integration in one or the other way as it is essential in converting larger and complex functions into manageable forms.
The topics covered in this Chapter are as follows:
1. Introduction
2. Integration as a reverse process of differentiation
3. Methods of Integration
4. Integrals of Some Particular Functions
5. Integration by Partial Functions
6. Integration by Parts
7. Definite Integral
8. Fundamental Theorem of Calculus
9. Evaluation of Definite Integrals by Substitution
10. Some Properties of Definite Integrals

Chapter 7 Maths Class 12 gives an overview of the history of differential calculus and the existence and development of integral calculus. In this chapter, students learn about the initial idea development of derivatives and the ways in which they solve the problem of defining tangent lines to the graphs of functions. This chapter also deals with the calculation of tangent lines’ slope.

NCERT Solutions For Class 12 Maths Chapter 7 will introduce the prime concept of integral calculus. This involves finding the area bounded by the graph of functions. Students learn the relationship between integration and differentiation and that integration is the reverse process of differentiation. Students are given a function in differentiation and are asked to figure out its differentiation. Oppositely, in integration, students are provided with the differential of a function and are asked to find the function.

The other important concepts include the following:

- The definition of indefinite integrals and how they are denoted;
- An overview of definite integrals;
- A look into the relationship between the fundamentals of indefinite integrals and definite integrals also called the fundamental theorem of calculus, which serves as a practical tool in engineering and science.

Examples:

- The derivative of x4 is 4x3, while the integral of 4x3 is x4.
- Similarly, the integral of 1/x is log I x I + C and the integral of cosx is sinx + C, where C is a constant.