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Really hard volume of rotation problem

  1. Jan 16, 2013 #1
    1. The problem statement, all variables and given/known data
    serocp.png


    2. Relevant equations
    Shell method


    3. The attempt at a solution
    Not sure if this is right, but the integral I set up is:
    [tex]2\pi \int_0^1 (4-y)(\sqrt{siny})dy[/tex]


    Finding the radius is my big problem with these problems, I cant visualize it very well.

    Any help is appreciated.
     
  2. jcsd
  3. Jan 16, 2013 #2

    SammyS

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    That looks fine except for the limits of integration.

    How did you get those limits?
     
  4. Jan 16, 2013 #3
    graphing [tex]\sqrt{siny}[/tex] from 0 to pi gives me a curve that goes to 1 and back to 0. Since I'm integrating wrt y, I figured it's 0 to 1?
     
    Last edited: Jan 17, 2013
  5. Jan 17, 2013 #4

    SammyS

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    You don't have [itex]\ \ y=\sqrt{\sin(x)}\ \ [/itex] with x going from 0 to π.

    You have [itex]\ \ x=\sqrt{\sin(y)}\ \ [/itex] with y going from 0 to π --- and your integration is w.r.t. y.
     
  6. Jan 17, 2013 #5
    Thanks, probably shouldn't agree with wolfram straight after I graph...
     
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