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