Mathematics

Problem

Determine the average value of the function

g(x)=\begin{cases} \sin x, & 0\le x<\tfrac{\pi}{2},\\ \dfrac{x}{2}, & \tfrac{\pi}{2}\le x\le \pi \end{cases}

over the interval

\left[\tfrac{\pi}{4},\,\tfrac{3\pi}{4}\right]

. Express your answer in terms of

\pi