Shell's Method: Solids of Rotation, Torus

[teken894]

Homework Statement

Volume of Torus: using Shell's mehod

$$4\pi \int^{1}_{-1}((R-x) \sqrt{r^2 - x^2})dx$$

Homework Equations

The Attempt at a Solution

I don't know how to integrate this at all. I cannot use any conventional methods...or I can't think of a way... i.e. use isolate a function as u and try to integrate wrt du

Is the only way to distribute the equation first?

 

[Tom1992]

try trig substitution, e.g. x=rcost or x=rsint. i did not complete it myself but that should work. after that you may need to do integration by parts. don't forget dx changes too, as does -1 and 1.