Chapter 14.8, Problem 16E

To determine

To prove: To verify that the integral ${\displaystyle \underset{R}{\int }{\displaystyle \int {\left(x+y\right)}^2{\sin }^2\left(x-y\right)}}dA\approx 2.363$; where R is the region bounded by the square with the vertices: $\left(0,1\right)$, $\left(1,2\right)$, $\left(2,1\right)$ and $\left(1,0\right)$.