Find charge density rho of a uniform shpere with radius R

[Andrew11]

Homework Statement

Find the potential V(r) inside and outside of a uniformly charged sphere with radius R and total charge q.
A) Fix first the charge density ρ(r) in the two regions 1: r>R and 2: 0<r<R the results should only be in terms of q and R[/B]

Homework Equations

ρ= qtot/Vtot
dq= ρ*Venc

The Attempt at a Solution

ρ= qtot/(4/3)piR^3
dq = [(qtot/(4/3)piR^3)*(4/3)pir^3]dr⇒(q*r^3/R^3)
∫dq = ∫q*(r^3/R^3)dr⇒ q*(¼r^4/R^3)

not sure if this is the correct approach to the problem

 

[mfb]

ρ= qtot/(4/3)piR^3

Don't forget brackets: ρ= qtot/((4/3)piR^3) or $\rho = \frac{3q}{4\pi R^3}$. Also, is this the charge density everywhere?
I don't understand what you are trying to do in the two lines below. You found the charge density, what does the integral mean and why do you integrate over a charge?