Very quick triple integral question

[narfarnst]

Homework Statement

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.

 

[tiny-tim]

hi narfarnst!

(have a square-root: √ )

… 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?

but it isn't √r !

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