Chapter 5.1, Problem 40E

In the following exercises, use property y. of double integrals and the answer from the preceding exercise to show that the following inequalities are true.

40. $\frac{1}{e^2}\le {\displaystyle \underset{R}{\iint }\sin x\cos ydA\le \frac{{\pi }^2}{48}}$ where $R=\left[0,1\right]\times \left[0,1\right]$