->     ^      ^
Compute the flux of the vector field F = xz i + yz j through the part of
the sphere x^2 + y^2 + z^2 = 9 oriented outward with x >= 0, y >= 0, z >= 0.

Answer z = f(x,y) form. Let D be x^2  + y^2 <= 9 in the 1st quadrant
->
dA = < x/sqrt(9-x^2-y^2), y/sqrt(9-x^2-y^2), 1>

->
F  = < x*sqrt(9-x^2-y^2), y*sqrt(9-x^2-y^2), 0>


flux = integral over D of x^2 + y^2 dA    -- switch to polar

integral theta=0..pi/2 integral r=0..3  r^3 dr d theta =

pi r^4 | 3     81 pi
--*--- |     = -----
2   4  | 0       8