Answer
$$\eqalign{
& \left( {\text{a}} \right){\text{Area}} = \int_0^2 {\int_{{y^2}}^{2y} {dxdy} } \cr
& \left( {\text{b}} \right){\text{Area}} = \int_0^4 {\int_{x/2}^{\sqrt x } {dydx} } \cr} $$
Work Step by Step
$$\eqalign{
& \left( {\text{a}} \right){\text{Area}} = \iint\limits_R {dx}dy \cr
& {\text{From the given graph}} \cr
& y = \sqrt x \Rightarrow x = {y^2} \cr
& y = \frac{x}{2} \Rightarrow x = 2y \cr
& {\text{The region }}R{\text{ is }}\left\{ {\left. {\left( {x,y} \right)} \right|{y^2} \leqslant x \leqslant 2y,{\text{ 0}} \leqslant y \leqslant 2} \right\},{\text{ Then}} \cr
& {\text{Area}} = \int_0^2 {\int_{{y^2}}^{2y} {dxdy} } \cr
& \cr
& \left( {\text{b}} \right){\text{From the graph}} \cr
& {\text{Area}} = \iint\limits_R {dy}dx \cr
& {\text{Area}} = \int_0^4 {\int_{x/2}^{\sqrt x } {dydx} } \cr} $$
