Integration is the reverse process of differentiation. It is also called anti-derivative.
Suppose the derivative of x5 is 5x4. Then the integration of 5x4 with respect to x is x5. we use this in symbol as follows:
Therefore for the above examples, we usually write
These integrals are also called improper integrals or indefinite integrals
Integrate the following with respect to x.
The above discussed integrals are known as improper integrals or indefinite integrals . For the proper or definite integrals we have the limiting points at both sides. These are called the lower limit and the upper limit of the integral.
This integral ∫(f)dx is an indefinite integral. Integrating the same function with in the given limits a and b is known as the definite integral. We write this in symbol as
In a definite integral where a is known as the lower limit and b is known as the upper limit of the definite integral. To find the value of definite integral, we do as follows:
Evaluate the following definite integrals: