Class 12 Maths Integrals Introduction

Introduction

Integral is one of the important concepts of calculus. Integral Calculus is motivated by the problem of defining and calculating the area of the region bounded by the graph of the functions as shown in the figure.

  Class_12_Maths_Integrals_Figure_1                                                                     

It is also used to find volumes, central points and many useful things.

The functions that could possibly have given function as a derivative are called anti derivatives or primitive of the function. Again, the formula that gives all these anti derivatives is called the indefinite integral of the function and such process of finding anti derivatives is called integration.

The development of integral calculus is used to solve the problems of the following types:

(a) The problem of finding a function whenever its derivative is given,

(b) The problem of finding the area bounded by the graph of a function under certain conditions.

These two problems lead to the two forms of the integrals, e.g., indefinite and definite integrals, which together constitute the Integral Calculus. The definite integral is also used to solve many interesting problems from various disciplines like economics, finance and probability.

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