Definite Integral of Cosx from 0 to Pi

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

The integration of the form

I =  \int\limits_0^\pi  {\cos xdx}

First we evaluate this integration by using integral formula \int {\cos xdx = \sin x} , then 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

\begin{gathered} \int\limits_0^\pi  {\cos xdx}   = \left| {\sin x} \right|_0^\pi \\ \Rightarrow \int\limits_0^\pi  {\cos xdx}   = \left[ {\sin \pi  - \sin 0}  \right] \\ \end{gathered}

From trigonometric values

\sin \pi  =  0

and \sin 0 = 0, we have

\begin{gathered} \Rightarrow \int\limits_0^\pi  {\cos xdx}   = \left[ {0 - 0} \right] \\ \Rightarrow \int\limits_0^\pi  {\cos xdx}   = \left[ 0 \right] \\ \Rightarrow \int\limits_0^\pi  {\cos xdx}   = 0 \\ \end{gathered}