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Evaluate triple integral, involves e -(x 2)

  1. Mar 4, 2012 #1
    Evaluate triple integral, involves e**-(x**2)

    1. The problem statement, all variables and given/known data
    Evaluate the triple integral of e**-(x**2 + 2y**2 + 3z**2), all of the limits are from -infinity to infinity.


    2. Relevant equations



    3. The attempt at a solution
    I'm not really sure how to do this problem. I know I have to change the coordinate system, but what to? I tried cylindricals, but it didn't seem right, unless I made a mistake there. Or do i have have to use spherical coordinates, which I am reading up on right now. Any help would be great.
     
  2. jcsd
  3. Mar 4, 2012 #2

    SammyS

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    Re: Evaluate triple integral, involves e**-(x**2)

    I would do it in rectangular coordinates. The integrand is of the form, f(x)g(y)h(z).

    Do you know the result for [itex]\displaystyle \int_{-\infty}^{+\infty}e^{-u^2}du\ ?[/itex]
     
  4. Mar 4, 2012 #3
    Re: Evaluate triple integral, involves e**-(x**2)

    I do not, and I imagine I will need some proof for my values so I don't think it's possible in cartesian coordinates unless I know the integral you stated. Is there an easy way to show proof for that integral?
     
  5. Mar 4, 2012 #4

    Dick

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    Re: Evaluate triple integral, involves e**-(x**2)

    http://en.wikipedia.org/wiki/Gaussian_integral
     
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