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**1. Homework Statement**

Use the Divergence Theorme to evaluate the flux of

**v**(x,y,z)=[tex]x^{2}[/tex]

**i**+[tex]y^{2}[/tex]

**j**+[tex]z^{2}[/tex]

**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.