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BASIC CONCEPTS OF INTEGRATION

When a function f(x) is known we can differentiate it to obtain its derivative

df/dx

The reverse process is to obtain the function f(x) from its derivative. This process is called INTEGRATION .  Applications of integration are numerous and some of these will be explained in subsequent  places. For now , what is important is that you practice basic  techniques and learn a variety of methods for integrating function.

INTEGRATION AS DIFFERENTIATION IN REVERSE

Suppose we differentiate the function y=x squared . We obtain dy/dx=2x. Integration reverses this process and we say that the integral of 2x is x squared. Practically, we can regard this as shown in Fig 1

This situation is just a little more complicqted because there are lots of functions we can differentiate  to give 2x. Here are some of them.