Hi, I've tried to solve this integral using cylindric coordinates but it seems very difficult. Any help is welcome.
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First, a comment there are no values of $z$ for which $\left(\frac{1}{2},\frac{1}{3},z\right)$ is in $\Omega $ once that is fixed it shouldn't be difficult to set up the integral in cylindrical coordinates
I tried this
Looks OK for the evaluation of the integral it may be easier to write $\displaystyle \sin \theta \sqrt{\sin ^2\theta -\cos ^2\theta }=\sin \theta \sqrt{1-2\cos ^2\theta }$
Originally Posted by Idea Looks OK for the evaluation of the integral it may be easier to write $\displaystyle \sin \theta \sqrt{\sin ^2\theta -\cos ^2\theta }=\sin \theta \sqrt{1-2\cos ^2\theta }$ Ok I try
Solved. Thank you