6.5 Average Value of a Function/2

$f(x)=\sin {(4x)}{\text{,}}\quad [-\pi ,\pi ]$

$f_{avg}={\frac {1}{\pi -(-\pi )}}\int _{-\pi }^{\pi }\sin {(4x)}\,dx={\frac {1}{2\pi }}\int _{-\pi }^{\pi }\sin {(4x)}\,dx$