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Method of shells around a different axis

  1. Sep 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Use the method of cylindrical shells to find the volume generated by rotation the region bounded by the given curves about the specified axis.

    2. Relevant equations

    y = x^2, y = 2-x^2; about x = 1
    3. The attempt at a solution

    I tried to just break it down.
    I want something of the form 2∏rhΔr
    OK so To find the height f(x) I subtracted.
    2-x^2-x^2 = 2-2x^2. For the radius I did a-x so 1-x is the radius

    So I have

    V = 2∏∫ (1-x)(2-2x^2)dx between -1 and 1 because that is where the graphs intersect.
    Evaluating it I got 2∏((x^4)/2 -(2x^3)/3 -x^2 +2x ] between -1 and 1

    I got 16∏/3
    Is this the right way?
  2. jcsd
  3. Sep 5, 2013 #2


    User Avatar
    Gold Member

    Yes, it is correct. Try doing it using disks and see if you can obtain the same answer. This will allow you to compare the complexity of the resulting integrals and see why one method is more efficient than the other in this case.
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