I need to solve this integral $$\int _0^1\:\int _{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\:\int _{\sqrt{x^2+y^2}}^1\:dzdydx$$ using spherical coordinates (I already made a sketch of the volume).
The problem is that I do not know my bounds for my integral in the spherical coordinates
I got
$$\int _0^{\pi }\:\int _{-\frac{\pi \:}{2}}^{\frac{\pi \:}{4}}\:\int _?^?\:r^2cos\delta \:drd\delta \:d\theta.$$
for my integral, I'm not really sure how to get my bounds for r.