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Homework Help: Shell Method Problem

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data
    x=y^(2), x=4, about the x axis.

    2. Relevant equations

    2pi* integral from a to b of radius*height of function*thickness

    3. The attempt at a solution
    I have 2pi* integral from -2 to 2 of y*(4-y^(2)) dy but that does not make any sense. Answer comes out to be 0. The real answer is 8pi. I know how to do this with the disk method just not the shell method. Thank for the help!!
    Last edited: Apr 10, 2012
  2. jcsd
  3. Apr 10, 2012 #2


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    hi hvidales! :smile:
    noooo :wink:
  4. Apr 10, 2012 #3
    I see and thanks. However, how come for this problem: y=x^(2), y=2-x^(2), about x=1 the limits are from -1 to 1 ?
  5. Apr 10, 2012 #4


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    you mean x goes from -1 to 1?

    that's because the body in that case goes from x = -1 to x = 3 (the reflection about x = 1)

    in your first example the body went from y = -2 to y = 2

    in each case, you're taking half (because each single cylindrical shell is in both halves) :wink:
  6. Apr 10, 2012 #5
    Thank you!!!
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