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Homework, triple integral

  1. Nov 27, 2006 #1
    my result of

    [tex] \int \int \int_{A} xyz dxdydz [/tex]


    [tex] A = \{(x,y,z); x^2+y^2+z^2 \leq 2, x \geq 0, y \geq 0, z \geq 0 \} [/tex]


    [tex] \frac {8}{48} [/tex],

    but book says

    [tex] \frac{1}{48} [/tex].

    Is the book right? Could you please verify?

    Thank you
  2. jcsd
  3. Nov 27, 2006 #2
    Hey Michael,

    I also got 8/48 using:

    [tex]x = \rho \sin\phi \cos\theta, y = \rho \sin\phi \sin\theta, z = \rho \cos\phi[/tex] with [tex] 0 < \phi < \frac{\pi}{2}, 0 < \theta < \frac{\pi}{2}, 0 < \rho < \sqrt{2}[/tex]

    so it looks to be correct, although I'd suggest checking everything one more time just to be sure.
    Last edited: Nov 27, 2006
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