Answer
\[\int_{0}^{2}{\int_{{{y}^{2}}}^{6-y}{f\left( x,y \right)dx}dy}\]
Work Step by Step
\[\begin{align}
& y=\sqrt{x}\Rightarrow x={{y}^{2}} \\
& x=6-y \\
& \text{From the graph, the region }R\text{ is} \\
& R=\left\{ \left( x,y \right):{{y}^{2}}\le x\le 6-y,\text{ 0}\le y\le 2\text{ } \right\} \\
& \text{Then,} \\
& \int_{0}^{2}{\int_{{{y}^{2}}}^{6-y}{f\left( x,y \right)dx}dy} \\
\end{align}\]
