How can I calculate one dimensional integration from three dimensional one?
Problem: Calculate flux of the vector field $F=(-y, x, z^2)$ through the tetraeder $T(ABCD)$ with the corner points $A= (\frac{3}{2}, 0, 0), B= (0, \frac{\sqrt 3}{2},0), C = (0, -\frac{\sqrt 3}{2},0), D = (\frac{1}{2},0 , \sqrt 2)$ by one dimensional integrtion.
I calculated div, where $divF = 2z$
I can see from the points distribution that $z\in [0,\sqrt 2] $ And according to theorem of Gauss I should apply this formula.
$\iiint_TdivFdv$
How can I seperate the integrals to get one dimensional?