# Very quick triple integral question

#### narfarnst

1. 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.

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#### tiny-tim

Homework Helper
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! 