Find the volume of the body $$ v:{(x,y,z) :\quad x^2+y^2\le z \le \sqrt{2-x^2-y^2}}.$$
I really don't know what to beside that i have to do triple integral of one.
My main problem is to understand the domains (do i need to use Jacobian?).
Thanks.
2026-03-28 19:30:15.1774726215
Multiple integral 3 dimension
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Hint
The graph shows in a 2D way the graph of $z$ (vertical axis) against $r=\sqrt{x^2+y^2}$. The blue shaded area is $z\ge r^2$, the other area is the other inequality. So you are interested in the overlap. You have to rotate it about the vertical axis (through the centre) to get the solid, whose volume you have to find.