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Revolution about horizontal and vertical lines

  1. Jan 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Use shell method to find volume.
    y=x+2
    y=x^2
    rotate about the x-axis




    2. The attempt at a solution

    I cannot seem to solve this. I thought this was the way to solve it, but I don't understand if I am missing something crucial.
    This is how I set up the integral.

    v=integral from 1 to 4 (2pi* y * (y-2-sqrt(y))
    This is not giving me the correct answer. Is this that way to set this up?
    I also tried the same integral from 0 to 4, and cannot determine what I am doing wrong.
    I would appreciate any help.
     
    Last edited: Jan 20, 2014
  2. jcsd
  3. Jan 20, 2014 #2

    tiny-tim

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    hi cathy! welcome to pf! :smile:
    let's see … you're using cylindrical shells of radius y, thickness dy, and length x2 - x1

    and that should be between where they meet, at (0,0) and at (2,4): ie for y between 0 and 4

    so you second try should work …

    can you show us your calculations? ​
     
  4. Jan 20, 2014 #3
    hello!
    well, i tried the second one again, like you said, and here are my calculations:

    taking the antideriv of,
    y^2-2y-y^3/2
    antideriv would be:
    1/3y^3 - y^2 - 2/5y^5/2
    plugging in 4, I get
    64/3 -16 -64/5 = -112/15 *2pi
    = -224/15pi
    and that is not correct

    Did I do something wrong here? Please advise.
     
  5. Jan 21, 2014 #4

    tiny-tim

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    (just got up :zzz:)

    looks ok (apart from everything being minus what it should be, since x2 > x+2) :confused:

    have you tried +224/15π ?
     
  6. Jan 21, 2014 #5
    Ohh. i actually see the problem. since it's required for me to do shells, the problem needed to be divided into two separate integrals.
    thank you for your help tiny-tim :)
     
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