# Definite Integral Inverse Tangent from 0 to Pi over 4

In this tutorial we shall derive definite integral of inverse tangent from limits 0 to Pi over 4.

The integration of the form

Here first function ${\tan ^{ - 1}}x$ and second function will be $1$, using formula for integration by parts in definite integral form, we have

Equation (i) becomes, we have

We using the basic rule of definite integral $\int\limits_a^b {f\left( x \right)dx = \left| {F\left( x \right)} \right|_a^b} = \left[ {F\left( b \right) - F\left( a \right)} \right]$, we have