Calculation of double integral. Calculate the double integral:
$$\int_{0}^{\frac{\pi^3}{8}}\; dx \int _{\sqrt[3] x}^{\frac{\pi}{2}}\; \cos\frac{2x}{\pi y}\;dy\;.$$
Can someone hint how to approach this as we have to integrate with respect to y but y is in denominator. I think the right approach might be changing it into polar co-ordinates but I am not able to set the limits.

Change the order of integral. We have
$$\int_0^{\pi^3/8} \int_{\sqrt[3]{x}}^{\pi/2} f(x,y)dydx = \int_0^{\pi/2} \int_0^{y^3} f(x,y) dx dy$$
Hope you can finish it from here.
