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