Answer
$${V_{avg}} = \frac{{20}}{{3\pi }}$$
Work Step by Step
$$\eqalign{
& {\text{The average velocity is given by }} \cr
& {V_{avg}} = \frac{1}{{\pi - 0}}\int_0^\pi {10\sin 3t} dt \cr
& {V_{avg}} = \frac{{10}}{\pi }\int_0^\pi {\sin 3t} dt \cr
& {\text{Integrate}} \cr
& {V_{avg}} = \frac{{10}}{{\pi \left( 3 \right)}}\left[ { - \cos 3t} \right]_0^\pi \cr
& {V_{avg}} = - \frac{{10}}{{3\pi }}\left[ {\cos 3t} \right]_0^\pi \cr
& {V_{avg}} = - \frac{{10}}{{3\pi }}\left[ {\cos 3\pi - \cos 0} \right] \cr
& {V_{avg}} = - \frac{{10}}{{3\pi }}\left( { - 1 - 1} \right) \cr
& {V_{avg}} = \frac{{20}}{{3\pi }} \cr} $$
