January 12th, 2019, 01:44 AM  #1 
Newbie Joined: Jan 2019 From: London Posts: 2 Thanks: 0  Double integral
How to evaluate this double integral: $\displaystyle \int_{x=0}^{x=\pi}\int_{y=0}^{y=2\pi}\frac{A^{2}B^ {2}C^{2}\sin x}{\left(A^{2}B^{2}\cos^{2}x+A^{2}C^{2}\sin^{2}x \sin^{2}y+B^{2}C^{2}\sin^{2}x\cos^{2}y\right)^{3/2}}dydx$ where $\displaystyle A,B,C$ are constants. 
January 12th, 2019, 09:04 AM  #2 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,621 Thanks: 117 
The x portion is of the form: $\displaystyle \int \frac{a\sin x}{(b +c\cos^{2} x)^{\frac{3}{2}}}dx$ Substitute u=cos x and look it up in a table of integrals. The rest should fall into place. 

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calculus, double, double integral, integral 
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