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A quick triple integral

  1. May 23, 2005 #1
    Firstly, can someone please demonstrate the proper Latex code for the terminals on a multiple integral? Thanks!

    Anyway, as you can probably see, i'm calculating the volume enclosed by x^2+y^2+z^2 = 2 and z = x^2+y^2 using a change to cylindrical coordinates.


    V = \iiint_{0}^{2\pi}_{0}^{\sqrt{2}}_{\rho^2}^{\sqrt{2-\rho^2}} \rho dz\,d\rho\,d\phi


    Is that integral right?

    The answer i get when evaluating the integral is (pi/3)(4sqrt(2) - 6), which is the same doing it by hand or using Mathematica. But it doesn't agree with the expected answer.
    Last edited: May 23, 2005
  2. jcsd
  3. May 23, 2005 #2


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    [tex] V=\int_{0}^{1}\rho \ d\rho \int_{0}^{2\pi} d\varphi \int_{0}^{\rho^{2}} dz [/tex]

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