Answer
\[\int_{0}^{23}{\int_{\frac{y-3}{2}}^{\frac{y+7}{3}}f(x,y) {dx}dy}\]
Work Step by Step
\[\begin{align}
& \text{Region bounded by: } \\
& y=2x+3\to x=\frac{y-3}{2} \\
& y=3x-7\to x=\frac{y+7}{3} \\
& \text{Let }y=y \\
& 2x+3=3x-7 \\
& x=10,\text{ }y=23 \\
& \text{From the graph, the region }R\text{ is} \\
& R=\left\{ \left( x,y \right):\frac{y-3}{2}\le x\le \frac{y+7}{3},\text{ }0\le y\le 23 \right\} \\
& \text{Then,} \\
& \int_{0}^{23}{\int_{\frac{y-3}{2}}^{\frac{y+7}{3}}f(x,y) {dx}dy} \\
\end{align}\]
