Chapter 14.2, Problem 14E

To determine

To calculate: The integral ${\displaystyle \underset{R}{\iint }\sin x\sin ydA}$ over the plane region R rectangle with vertices $\left(-\pi ,0\right),\left(\pi ,0\right),\left(\pi ,\frac{\pi }{2}\right)$ and $\left(-\pi ,\frac{\pi }{2}\right)$.