Answer
$\frac{\sqrt 2}{\pi}$.
Work Step by Step
1. Given $f(x)=sin(\frac{x}{2})$, we have $f(0)=sin(\frac{0}{2})=0$ and $f(\frac{\pi}{2})=sin(\frac{\pi}{4})=\frac{\sqrt 2}{2}$.
2. We have the average rate of change as $R=\frac{f(\frac{\pi}{2})-f(0)}{\frac{\pi}{2}-1}=\frac{\frac{\sqrt 2}{2}}{\frac{\pi}{2}}=\frac{\sqrt 2}{\pi}$.
