Answer
\[\int_{0}^{2}{\int_{0}^{{{x}^{2}}}{f\left( x,y \right)}dydx}\]
Work Step by Step
\[\begin{align}
& \int_{0}^{4}{\int_{\sqrt{y}}^{2}{f\left( x,y \right)}dxdy} \\
& \text{Using the graph to switch the order of integration} \\
& 0\le y\le {{x}^{2}} \\
& 0\le x\le 2 \\
& \text{Then} \\
& \int_{0}^{2}{\int_{0}^{{{x}^{2}}}{f\left( x,y \right)}dydx} \\
\end{align}\]
