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Limit of this integral

  1. Aug 22, 2012 #1
    1. The problem statement, all variables and given/known data


    The problem is attached in the picture.

    3. The attempt at a solution

    My question is, why can't the limits of ∫(dp) be from 0 to 1?

    The shape is of the body is an inverted cone of angle 45 degree. Then isn't the question simply to find the integral of that function from p = 0 to p = 1, z = 0 to z = 1 and ∅ = 0 to ∅ = 2∏?

    Since:

    x = p cos∅
    y = p sin∅
    z = z


    x2+y2 ≤ z2, 0 ≤ z ≤ 1

    p2 ≤ z2

    p ≤ z
     

    Attached Files:

  2. jcsd
  3. Aug 22, 2012 #2

    SammyS

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    Doing what you suggest would be integrating over a right circular cylinder of radius 1 and height of 1.
     
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