Exercise 43

Evaluate the integral by changing to spherical coordinates. \[ \int_{-2}^2 \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{2-\sqrt{4-x^2-y^2}}^{2+\sqrt{4-x^2-y^2}} (x^2+y^2+z^2)^{3/2} \, dz \, dy \, dx \]