Chapter 13.1, Problem 30E

Choose a convenient order When convened to an iterated integral, the following double integrals are easier to evaluate in one order than the other. Find the best order and evaluate the integral.

30.     ${\displaystyle \underset{R}{\iint }{y}^3\sin x{y}^{2}dA;R=\left\{\left(x,y\right):0\le x\le 2,0\le y\le \sqrt{\pi /2}\right\}}$