Answer
\[\int_{1}^{4}{\int_{0}^{4-y}f(x,y) {dx}dy}\]
Work Step by Step
\[\begin{align}
& y=4-x,\text{ }y=1,\text{ }x=0 \\
& y=4-x\to x=4-y \\
& \text{From the graph, the region }R\text{ is} \\
& R=\left\{ \left( x,y \right):0\le x\le 4-y,\text{ }1\le y\le 4\text{ } \right\} \\
& \text{Then,} \\
& \int_{1}^{4}{\int_{0}^{4-y}f(x,y) {dx}dy} \\
\end{align}\]
