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Evaluating a triple integral Spherical

  1. Nov 8, 2013 #1
    1. The problem statement, all variables and given/known data
    z(x^2+y^2+z^2)^(-3/2) where x^2+y^2+z^2 ≤ 4 and z ≥ 1





    3. The attempt at a solution
    So spherically this comes down to cos∅sin∅dpdθd∅
    p goes from 0 to 2, theta goes from 0 to 2pi, but I don't know how to figure out what ∅ goes from? i'm trying use trig identities but i'm getting the wrong answer, so maybe this don't work since the sphere is curved?
     
  2. jcsd
  3. Nov 8, 2013 #2

    vela

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    Your limits for ##\rho## aren't correct. For example, consider the part of the z-axis which is inside the solid. It's only the part where 1 ≤ z ≤ 2. This would be inconsistent with ##\rho \le 1##, yet your lower limit for ##\rho## is 0.

    In this case, you have cylindrical symmetry, so try drawing a cross section of the surface through, say, the xz plane. You should be able to see pretty easily the limits of ##\phi##, and you'll have to figure out the limits of ##\rho## as a function of ##\phi##.
     
  4. Nov 8, 2013 #3

    haruspex

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    Given the bounds, it might be easier to handle in cylindrical.
     
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