# Shell's Method: Solids of Rotation, Torus

1. Jan 16, 2007

### teken894

1. The problem statement, all variables and given/known data

Volume of Torus: using Shell's mehod

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

2. Relevant equations

3. 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?

Last edited: Jan 16, 2007
2. Jan 16, 2007

### 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.

Last edited: Jan 16, 2007