Triple Integral with Exponential and Radical Functions

[HclGuy]

Homework Statement

Find $$\int\int\int\sqrt{x^2+y^2+z^2}e^{-x^2-y^2-z^2}dxdydz$$
The limits of integration for all 3 variables are from -infinity to infinity.

Homework Equations

This one has me completely stumped, so I'm just wondering if someone could push me in the right direction in how to solve this one. I thought about maybe finding a suitable substitution for the region of integration but I'm not sure at how that might work.
Thanks

 

[tiny-tim]

Homework Statement

Find $$\int\int\int\sqrt{x^2+y^2+z^2}e^{-x^2-y^2-z^2}dxdydz$$
The limits of integration for all 3 variables are from -infinity to infinity.

Hi HclGuy!

Hint: change the variables of integration from x y and z to … ?

 

[HclGuy]

Are you hinting towards spherical coordinates...?
I'm going to try that out.. Thanks

 

[rocomath]

becomes trivial once you change variables

 

[HclGuy]

Thanks guys, got it now.