Answer
$$R = \left\{ {\left( {r,\theta } \right):0 \leqslant r \leqslant 8,{\text{ 0}} \leqslant \theta \leqslant \pi } \right\}$$
Work Step by Step
$$\eqalign{
& {\text{The represented region }}R{\text{ is a semicircle of radius 8}}{\text{. It can }} \cr
& {\text{be described in polar coordinates as:}} \cr
& R = \left\{ {\left( {r,\theta } \right):0 \leqslant r \leqslant 8,{\text{ 0}} \leqslant \theta \leqslant \pi } \right\} \cr} $$
