Answer
\[\int_{0}^{18}{\int_{y/2}^{y/3+3}f(x,y) {dx}dy}\]
Work Step by Step
\[\begin{align}
& y=2x\to x=\frac{1}{2}y \\
& y=3x-9\to x=\frac{1}{3}y+3 \\
& \text{From the graph, the region }R\text{ is} \\
& R=\left\{ \left( x,y \right):\frac{1}{2}y\le x\le \frac{1}{3}y+3,\text{ }0\le y\le 18 \right\} \\
& \text{Then,} \\
& \int_{0}^{18}{\int_{y/2}^{y/3+3}f(x,y) {dx}dy} \\
\end{align}\]
