I need to solve:
Calculate the volume bounded by the surface
$$ (x^2+y^2+z^2)^2 = x $$
and not sure on how to do it.
If I move to spherical coordinates, I get that the equation gives: $$ r^4=r\sin(\phi) \cos(\theta ) \Rightarrow r^3 = \sin(\phi) \cos(\theta ) $$ but I have no idea how to obtain the boundaries of integration from this... Will you help me ?
I understand that probably: $0\leq r \leq \sqrt[3]{\sin(\phi) \cos(\theta )}$ , and that $0\leq \phi \leq \pi$, but what about $\theta$ ?
Thanks a lot in advance