# Very quick triple integral question

1. May 5, 2010

### narfarnst

1. The problem statement, all variables and given/known data
Use the Divergence Theorme to evaluate the flux of v(x,y,z)=$$x^{2}$$i+$$y^{2}$$j+$$z^{2}$$k on the solid T bounded above by a sphere with radius 3 and below by the xy-plane.
I've found that div(v) is 2(x+y+z).

When I go to set up the integral I get a triple integral over T of (x+y+z)dV (and I bring the 2 outside the integral). So, of course, I switch to spherical coordinates.
Now, my question. When I do the switch, can I treat (x+y+z) as sqrt(r), or do I actually have to plug in the parametrized x, y, and z and evaluate?

Thanks.

2. May 5, 2010

### tiny-tim

hi narfarnst!

(have a square-root: √ )
but it isn't √r !

so, yes, you do actually have to do the work!