Solving Volume Problems in Physics: Cartesian vs. Spherical Coordinates

[twoflower]

Hi,

been solving another volume problem here and though it seemed very straightforward, I'm getting very ugly integrals so it rather seems that I haven't chosen appropriate approach. I scanned how I did it, first in cartesian coordinates:

http://twoflower.matfyz.cz/inc/int.cartesian.jpg"

and then in spherical coordinates:

http://twoflower.matfyz.cz/inc/int.polar.jpg"

Neither of them seems useful...or maybe I'm substituting it wrongly.

A is the set the volume of which I'm trying to compute.

Thank you for any advices.

 

[twoflower]

I got it, I really didn't choose the best approach.