Convert the integral from rectangular cordinates to both cylinderical and spherical coordinates, and evaluate the simplest iterated integral.
http://www.wolframalpha.com/input/?i=integral+x+dz+dy+dx+from++x%3D-2+to+2%2Cy%3D+-%284-x%5E2%29%5E1%2F2+to+%284-x%5E2%29%5E1%2F2%2Cz%3Dx%5E2%2By%5E2+to+4

Question

Convert the integral from rectangular cordinates to both cylinderical and spherical coordinates, and evaluate the simplest iterated integral.
http://www.wolframalpha.com/input/?i=integral+x+dz+dy+dx+from++x%3D-2+to+2%2Cy%3D+-%284-x%5E2%29%5E1%2F2+to+%284-x%5E2%29%5E1%2F2%2Cz%3Dx%5E2%2By%5E2+to+4

anonymous · Answer

setting up the cylindrical one wasn't difficult I'm just having issues with getting the limts for the spherical one.

anonymous · Answer

$$\int\limits_{-2}^{2}\int\limits_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}\int\limits_{x^2+y^2}^{4}(x)  d x d y d x$$

anonymous · Answer

$$\int\limits_{}^{}\int\limits_{}^{}\int\limits_{}^{}p^3 \sin^2 \phi \cos \theta dp d \phi d \theta$$
^this is the conversion of the functio itself.

anonymous · Answer

This is a diagram I found that might help:

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