Easy gauss' law question that I wanna make sure I didn't make too easy

schattenjaeger

A sphere of radius a has its center at the origin, and has charge density p=Ar^2

another sphere of radius = 2a is concentric with the first. Find the flux SE*da through the larger sphere, where that's the surface integral of E dot da, like usual. It'd just be Qin/e where e is that constant, right? So I just have to do that volume integral that ends up having integrand Ar^2sin(theta) with r going from 0 to a, theta from 0 to pi, phi from 0 to 2pi?

And though it's not asked, if I DID wanna find the electric field I'd note that da vector is r-hat*da and E only has the radial dependency, so Evector=Er*r-hat

so you end up with Er16pi*a^2=Qin/e solve for Er?