Wednesday 29 July 2015

calculus - How to show that $int_0^{pi/2}int_0^{pi/2}left(frac{sinphi}{sintheta}right)^{1/2},dtheta,dphi=pi$?

$$\int_0^{\pi/2}\int_0^{\pi/2}\left(\frac{\sin\phi}{\sin\theta}\right)^{1/2}\,d\theta\,d\phi=\pi$$
Indeed, I tried to solve this integral by complexifying (using Euler's formula) the $\sin\theta$ and $\sin\phi$.But it didn't work because I faced the exponent which would make things difficult to tackle such integral.



I would appreciate any suggestions for solving this integral.

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