Class | XII |

Subject | Mathematics – ENG |

Chapter | VII – Integrals |

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## Ncert Class 12 Maths Chapter 7 Solutions – Integrals

## Integrals – Introduction

Differential calculus focuses on the concept of derivatives. The basic motivation for derivatives was the problem of defining tangent lines for graphing functions and calculating the slope of such lines. Integral calculus is driven by the problem of defining and calculating the area surrounded by graphs of functions

If a function f interval is incalculable in I, that is, its differential exists at every point of the f I, then a natural question arises: can we determine the function that is f at every point of I?

Functions that could act as derivatives are called the deprecation (or primitive) of the function. Moreover, the formula that gives all these deprecations is called ** indefinite integration** of function, and such process of determining the recalculation is called integration.

In many practical situations, such problems arise. For example, if we know the immediate velocity of something at any moment, a natural question arises, that is, can we determine the position of the object at any moment? There are many practical and theoretical situations where the process of integration is involved.

The development of integration arises from efforts to solve the following types of problems:

- The problem of finding a function whenever it is derived,
- The problem of finding an area surrounded by a function graph under certain conditions.