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Solids of revolution question

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid generated by rotating about the y-axis
    y= 1-x3 x=0 , y=0

    I tried sketching the graph of y= 1-x^3 then tried to find the volume from y=1 to y=0.

    if x^3 = 1-y
    x= (1-y)1/3
    so x2= (1-y)2/3

    ∏∫x2δy

    => ∏∫(1-y)2/3.dy = ∏[ -3/5(1-y)^(5/3)]

    I did that for y=1 to y=0.
    But I can't get the right answer.

    I got 0pi
    but the answer should be 3pi/5
     
    Last edited: Feb 20, 2013
  2. jcsd
  3. Feb 20, 2013 #2

    eumyang

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    It would be helpful if you told us what answer you got and what answer you are supposed to get.
     
  4. Feb 20, 2013 #3
    I edited it
     
  5. Feb 20, 2013 #4

    eumyang

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    The antiderivative looks right, so it looks like the error is in substituting the y = 1 and y = 0. Double check your work.
     
  6. Feb 20, 2013 #5
    omg I'm so stupid I didn't do the one for 0, because most times when it's 0 I ignore it. Bad a habit. I got 3/5pi now
     
    Last edited by a moderator: Feb 20, 2013
  7. Feb 20, 2013 #6

    haruspex

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    What did you get for each bound (y=0, y=1)?
     
  8. Feb 20, 2013 #7
    I got it now!
     
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