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Integration

Integration is the inverse operation of differentiation.

 

Let y = f (x) be a function of x. The derivative of y with respect to x is given by Description: 82016.png

 

Therefore, the integral of f ′(x) with respect to x is given byDescription: 82030.png

 

This type of integration is done without any defined values for the variable x. Hence, it is known as indefinite integration. We need to add a constant of integration ‘c’ to the final result in case of indefinite integration.

Some Basic Results

Sl. No.

Function

Integral

1.

Description: 82067.png

x + c

2.

Description: 82073.png

Description: 82079.png

3.

Description: 82085.png

loge x + c

4.

Description: 82093.png

Description: 82107.png

5.

Description: 82169.png

Description: 82175.png

Where c is called the constant of integration.





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