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Help with yet another solid of revolution question

  1. Jan 28, 2014 #1
    1. The problem statement, all variables and given/known data

    See the attached problem.


    2. Relevant equations

    See the attached problem.


    3. The attempt at a solution

    I used washer method and got an inner radius of x=y^2 and an outer radius of x=y+2, I calculated my upper limit as being 4 and my lower limit as being 0. The answer is 72π/5, but I can't seem to get that answer. Are my limits of integration wrong and/or did I use the wrong method?
     

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  2. jcsd
  3. Jan 28, 2014 #2

    haruspex

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    That method works for me. Please post your detailed steps.
     
  4. Jan 28, 2014 #3
    V=π∫(y+2)^2 - (y^2)^2 dy, from 0 to 4
    V= -2032π/15, which is obviously not the correct answer since volume can't be negative etc.
     
  5. Jan 28, 2014 #4

    haruspex

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    Right integrand, wrong range. x goes from 0 to 4. what's the range for y?
     
  6. Jan 28, 2014 #5
    I set √x=x-2, and solved the quadratic and got x=4,1 (I used the 4 as my upper limit and used 0 as my lower limit since it seemed that 0 was the lower limit from how the graph looked). Also how exactly do I go about calculating the limits of integration in regards to y?
     
  7. Jan 28, 2014 #6

    haruspex

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    Yes, but you are integrating with respect to y, so your bounds must be bounds on y, not x.
    Sketch the curves and see where they cross.
     
  8. Jan 28, 2014 #7
    I set the equations equal and I get my upper limit as 4 with respect to y and my lower limit as 1 with respect to y, however I still don't get the correct answer which is 72π/5.
     
    Last edited: Jan 28, 2014
  9. Jan 28, 2014 #8
    So I finally realized I was supposed to solve y^2=y+2 and get an upper and lower limit of 2 and -1 respectively. After plugging in those two values into the integrand, I finally ended up getting the correct answer. Thanks for the help.
     
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