Answer
\[\int_{-4}^{5}{\int_{-y/3+5/3}^{\sqrt{25-{{y}^{2}}}}f(x,y) {dx}dy}\]
Work Step by Step
\[\begin{align}
& x=\sqrt{25-{{y}^{2}}} \\
& y=-3x+5\to x=-\frac{1}{3}y+\frac{5}{3} \\
& \text{From the graph, the region }R\text{ is} \\
& R=\left\{ \left( x,y \right):-\frac{1}{3}y+\frac{5}{3}\le x\le \sqrt{25-{{y}^{2}}},\text{ }-4\le y\le 5 \right\} \\
& \text{Then,} \\
& \int_{-4}^{5}{\int_{-y/3+5/3}^{\sqrt{25-{{y}^{2}}}}f(x,y) {dx}dy} \\
\end{align}\]
