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Homework Help: Question involving the shell method

  1. May 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the given axis:

    y = x2, y = 0, x = 1, x = 2, about x = 1

    2. Relevant equations

    V = 2[itex]\pi[/itex][itex]\int[/itex]xf(x)

    3. The attempt at a solution

    I am assuming based off the graph that my f(x) would be equal to 4-x2, but I am having difficulty figuring out the respective x value. Any help?
  2. jcsd
  3. May 22, 2012 #2


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    Science Advisor

    Then I suggest you look at your graph again! Each shell, at a specific x, has a length ranging from y= 0 to [itex]y= x^2[/itex] so that its height is [itex]x^2- 0= x^2[/itex].
  4. May 22, 2012 #3
    Wow... that was silly of me. That makes a lot more sense. So I would integrate 2[itex]\pi[/itex][itex]\int[/itex](x-1)(x2)dx from 1 to 2, which gives me an answer of 17/2. Thanks for the help.
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