# The Definite Integral of Sinx from 0 to Pi

In this tutorial we shall derive the definite integral of the trigonometric function sine from limits 0 to Pi.

The integration of the form is

First we evaluate this integration by using the integral formula $\int {\sin xdx = - \cos x}$, and then we use the basic rule of the definite integral $\int\limits_a^b {f\left( x \right)dx = \left| {F\left( x \right)} \right|_a^b} = \left[ {F\left( b \right) - F\left( a \right)} \right]$. So we have

From the trigonometric values $\cos \pi = - 1$ and $\cos 0 = 1$, we have