Convert to spherical coordinates and evaluate:$$\iiint_{E}z(x^2+y^2+z^2)^{-3/2}dV$$ where E is the region satisfying the following inequalities:$$x^2+y^2+z^2\le16,z\ge 2$$ This is what i have done so far.
$$E=(\rho,\theta,\phi):0\le\phi\le\pi/3, 0\le\theta\le2\pi, 2/cos\phi\le\rho\le4$$
$$\int_{0}^{2\pi}\int_{0}^{\pi/3} \int_{2/cos\phi}^{4} \cos\phi\sin\phi \ d\rho d\phi d\theta\ = (\int_{0}^{2\pi} d\theta) (\int_{0}^{\pi/3} \rho \ cos\phi\sin\phi |_{\rho= 2/cos\phi}^{\rho=4} \ d\phi)$$
Can anyone check if this is correct please.