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Triple integrals, Find Volume

  1. Jun 7, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid bounded above by [tex]\rho[/tex]=1+cos[tex]\varphi[/tex] and below by [tex]\rho[/tex]=1

    2. Relevant equations


    3. The attempt at a solution

    I already solved it but was comparing my answer to my professor's solution, I was wondering why when he did the integration, his limits for [tex]\rho[/tex] were from 0 to 1, wouldn't the limits for rho be 1 to 1+cos[tex]\varphi[/tex]? Thanks
     
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  3. Jun 7, 2008 #2

    HallsofIvy

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    There are any number of reasons why one integral might give the same result as another- since you did not post his complete integral I don't believe we can say why his method works for this particular problem.
     
  4. Jun 7, 2008 #3
    The thing is, I got a different answer and was not sure if the professor had made an error on the answer key since I already spotted a few other errors on it..but lets see now
    [tex]\int\int_0^\pi\int_0^1\rho^2\sin\varphi d\rho d\varphi d\theta[/tex]
    outer limits are from 0 to 2pi
    I was just wondering why his limits for [tex]\rho[/tex] were from 0 to 1. I thought it would be from 1 to 1+cos[tex]\varphi[/tex]
     
  5. Jun 7, 2008 #4

    HallsofIvy

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    You may have copied the problem wrong or he may have set it up wrong himself. Have you asked your professor?
     
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