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Shell's Method: Solids of Rotation, Torus

  1. Jan 16, 2007 #1
    1. The problem statement, all variables and given/known data

    Volume of Torus: using Shell's mehod

    [tex] 4\pi \int^{1}_{-1}((R-x) \sqrt{r^2 - x^2})dx [/tex]

    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. jcsd
  3. Jan 16, 2007 #2
    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
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