1. ## Help triple integral

Hi,
I've tried to solve this integral using cylindric coordinates but it seems very difficult.
Any help is welcome.

2. ## Re: Help triple integral

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

4. ## Re: Help triple integral

Looks OK

for the evaluation of the integral it may be easier to write

$\displaystyle \sin \theta \sqrt{\sin ^2\theta -\cos ^2\theta }=\sin \theta \sqrt{1-2\cos ^2\theta }$

5. ## Re: Help triple integral

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

6. ## Re: Help triple integral

Solved. Thank you