This is an exercise in using spherical coordinates.
Calculate the triple integral
$$J = \iiint_{Q}\ \frac{1}{x^2+y^2+z^2} \,dx \,dy \,dz$$
where $Q$ is the body between the two spheres
$$x^2+y^2+z^2 = 1 $$ and
$$x^2+y^2+z^2 = 9 $$
The calculation is quite easy.
I am getting answer $8\pi$ but the answer given is $4\pi$.
Which one is correct?
Use the system of spherical coordinates (following a physicist notation) to obtain
$$ J = \int_1^3 \int_0^{2\pi} \int_0^\pi \frac{1}{r^2} \, r^2 \sin\theta \, \mathrm{d} \theta \, \mathrm{d} \phi \, \mathrm{d} r = 8\pi $$
If they get $4\pi$, then the polar angle has only been integrated between $0$ and $\pi/2$, i.e., by considering the upper volume only.