Computing Integral - ball

I have this question attached.

Attachment 30565

Spherical*

I'd really recommend doing this in spherical coordinates.

$x^2+y^2 \to \rho^2 \sin^2(\theta)$

$dx~dy~dz~ \to \rho^2 \sin(\theta) d\rho~d\theta~d\phi$

$0 \leq \rho \leq d$

$0 \leq \theta \leq \pi$

You can see that $\phi$ doesn't appear in the integral anywhere so integration over $\phi$ just adds a factor of $2 \pi$

you should be able to manage it from here.