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Shell Method Setup

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data
    use the shell method to find the volume of the solid given by y = 4x - x2 y = x2, about the line x = 4

    3. The attempt at a solution
    I have to find a height and a radius multiply them together and integrate them over some bounded region, fair enough. My functions intersect at x = 2 and x = 0, my bounds have been set. I have to find my height, which I believe to be "x", and my radius. I believe that to be my top function, 4x - x2 - my bottom function, x2 so I multiply them within my integrand to get 4x2 - 2x3 after integrating I get 4x3/3 - x4 / 2. Evaluating this expression at x = 2 I get 32/3 - 24/3 multiplied by 2pi to get 16pi/3. My book tells me it is 16pi so I went back and looked at this a few times and did the calculation over and i'm getting the same answer and i'm not sure where i'm getting this wrong with my geometry.
     
  2. jcsd
  3. Feb 19, 2013 #2

    Dick

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    Your height is 4x-2x^2. Your radius isn't x. You are rotating around x=4. What is it?
     
  4. Feb 19, 2013 #3
    *sigh* 4-x
     
  5. Feb 19, 2013 #4

    Dick

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    Riiighht.
     
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