Integration is used in dealing with two essentially di?erent types of problems:
The ?rst types are problems in which the derivative of a function, or its rate of change, or the slope of its graph, is known and we want to ?nd the function. We are therefore required to reverse the process of di?erentiation. This reverse process is known as anti-differentiation, or ?nding a primitive function or ?nding an indefinite integral.
The second type leads to the de?nition of the definite integral. De?nite integrals are used for ?nding area, volume, centre of gravity, moment of inertia, work done by a force, and in many other applications.
This integral is called an indefinite integral because its value is not fully determined until the endpoints are specified. This ambiguity is dealt with by the addition of the constant C at the end. This constant of integration is added to the end because there are, in fact, an infinite number of solutions to the integral.
From exam point of view the whole category of integrals are widely used in modern sciences as well as in engineering entrance examinations. They account to many lengthy numericals and key derivations.