Evaluate triple integral, involves e -(x 2)

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

Homework Statement


Evaluate the triple integral of e**-(x**2 + 2y**2 + 3z**2), all of the limits are from -infinity to infinity.


Homework Equations





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.
 

Answers and Replies

  • #2
SammyS
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Homework Statement


Evaluate the triple integral of e**-(x**2 + 2y**2 + 3z**2), all of the limits are from -infinity to infinity.

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.
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]
 
  • #3
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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?
 
  • #4
Dick
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