How to integrate this using cylindrical coordinates:
$$\int_{-1}^1\int_{-\sqrt{1-y^2}}^1\int_{-1}^1(x^2+y^2)^{3/2}\,dz\,dx\,dy$$
Now what I can understand is that we can directly integrate the $z$ part. Now I am confused in transferring the $x$ part from $(x,y,z)$ to $(r,\theta,z)$ as here $\theta$ will vary from $0$ to $2\pi$ but what about the $r$ part?
Please help.