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Homework Help: Trouble finding volume of curve shell method

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Given the following curve:
    y = x^3
    Use shell method and rotate around x-axis to determine the volume
    bounded region: y = 8, x = 0

    2. Relevant equations

    3. The attempt at a solution
    x(x^3) = x^4
    x^4 = 1/5 x^5
    1/5(8)^5 = 6553.6
    *2 = 13107.2 pi

    the answer should be 768/7 pi, where did I go wrong? thanks.
    Last edited: Feb 19, 2013
  2. jcsd
  3. Feb 19, 2013 #2


    Staff: Mentor

    What is the complete problem statement? You need to have some finite region in the plane to start with.
  4. Feb 19, 2013 #3
    bounded region: y = 8, x = 0
  5. Feb 19, 2013 #4


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    Homework Helper

    For starters, if you are supposed to use shell method, revolving around the x-axis, than the integrand needs to be in terms of y, not x.
  6. Feb 19, 2013 #5


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    Science Advisor
    Homework Helper
    Gold Member

    As eumyang notes, you've used the disc method, not the shell method, but it still should produce the right answer. Your answer is wrong because you've calculated the wrong region. It is not bounded by y=0, it's bounded by y=8. Draw the bounded region in the XY plane.
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