Energy of Coaxial Cylindrical Shells

[NeedPhysHelp8]

Homework Statement

Calculate the energy per unit length for two long coaxial cylindrical shells, neglecting end effects. The inner and outer cylinders have radii a and b, and linear charge densities λ and -λ, uniformly distributed on the surface, respectively.

2. The attempt at a solution

Alright so first thing I did was calculate the electric field in various regions using Gauss' Law:
i) for r<a E=0
ii) for a<r<b E=\frac{\lambda}{2\pi \epsilon r}
iii) for r>b E=0

Now I'm not too sure how to find the energy per unit length: we have the formula E=1/2 \int \lambda V \ dl so should I just find the potential V(r) then sub it into that equation?
I can find V(r) by \int E \ dl

 

[Kyxha]

Haha Phys 400? I am having similar trouble...