Chapter 15: Multiple Integrals - Section 15.1 - Double and Iterated Integrals over Rectangles - Exercises 15.1 - Page 875: 32

since the integral of the odd function x over an interval symmetric to 0 is equal to 0

$\int^{\frac{\pi}{2}}_{0} sin(\sqrt{y})dy$ is some number, say a then $\int^{1}_{-1} \int^{\frac{\pi}{2}}_{0} xsin\sqrt{y} =a \int^{1}_{-1}xdx=0$ since the integral of the odd function x over an interval symmetric to 0 is equal to 0