Answer
\[\text{Graph}\]
Work Step by Step
\[\begin{align}
& \int_{-2}^{2}{\int_{{{x}^{2}}}^{4}{{{e}^{xy}}}dydx} \\
& \text{Let the functions} \\
& y={{x}^{2}}\text{ and }y=4 \\
& -2\le x\le 2 \\
& \text{Then, the region }R\text{ is} \\
& R=\left\{ \left( x,y \right):{{x}^{2}}\le y\le 4,-2\le x\le 2 \right\} \\
& \text{Graph} \\
\end{align}\]