Opinion? Solids of Revolution/Integration Techniques

[Newbatmath]

Homework Statement

Hey everyone. In my calc course I need to create (or find on the web) a problem and apply the below two concepts that I learned in the class.

Concepts:
Solids of Revolution.
Integration Techniques: Parts, Substitution, or Partial Fractions.

Homework Equations

The problem I chose was:

http://curvebank.calstatela.edu/volrev/vase7.gif

The Attempt at a Solution

Well, the question I am asking is basically if this equation I found can be solved using one of the Integration Techniques. I was thinking Parts. Would that be right?

 

[rock.freak667]

Just expand it out. Then use the double angle formula for cos2x, to replace sin²x

 

[Newbatmath]

So One of the Integration Techniques can't be used, then?

 

[rock.freak667]

Integration by parts might make it more complex, substitution, I don't think will work and you can't split it into partial fractions.

 

[Newbatmath]

Well, cruds.

Thank you! I'm off to find another problem then I guess. They did say I could also choose arc lengths. Maybe I'll go with that...