Evaluate triple integral, involves e -(x 2)

[MeMoses]

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.

 

[SammyS]

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 $\displaystyle \int_{-\infty}^{+\infty}e^{-u^2}du\ ?$

 

[MeMoses]

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?

 

[Dick]

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?

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