# Challenging triple integral

1. Jun 9, 2008

### HclGuy

1. The problem statement, all variables and given/known data

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.

2. Relevant 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

2. Jun 9, 2008

### tiny-tim

Hi HclGuy!

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

3. Jun 9, 2008

### HclGuy

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

4. Jun 9, 2008

### rocomath

becomes trivial once you change variables

5. Jun 9, 2008

### HclGuy

Thanks guys, got it now.