Chapter 13.5, Problem 74E

Charge distribution A spherical cloud of electric charge has a known charge density Q(ρ), where ρ is the spherical coordinate. Find the total charge in the interior of the cloud in the following cases.

a.     $Q\left(\rho \right)=\frac{2\times {10}^{-4}}{{\rho }^4},1\le \rho <\infty$

b.     $Q\left(\rho \right)=\left(2\times {10}^{-4}\right)e^{-0.01{\rho }^3},0\le \rho <\infty$