I suggest you switch to spherical coordinates as soon as possible. Review the section in your book on spherical coordinates. In particular, you should know how to describe half a sphere and that the Jacobian in spherical coordinates is . In this case you'll have (assuming the ball is as you've graphed it).
Spherical coordinate system - Wikipedia, the free encyclopedia
i tried to solve it like this but i got a bad resolt where is my mistake?
where is my mistake why i get 0
TheEmptySet told you where the error lies. I used the symbols from the Wikipedia article where a unit sphere is .
You have switched the limits for and .
not 2 pi
I was referring to the unit sphere.
What you posted is only correct if the Jacobian for the spherical coordinates in this problem is . Again, read the Wikipedia article I linked to if you're confused about the symbols used.