Your R (outer radius) is simply the function because your axis of rotation is the x-axis.
Your answer becomes:
Hope I helped
Do you get it now?
Well, this is actually a non-elementary integral. This is impossible to compute normally. If you are more advanced in calculus you can do it, though. Do you know Dawson's function?
Well the answer to the indefinite integral is where F is the Dawson Function. Yeah, a first (or even second) year calc student would not be responsible for being able to do this integral. Are you sure you weren't allowed to use a graphing calculator?