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I need help finding the flux through an ellipsoid (the surface) where F=
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Div(F)=2 x + 4 y + 6 z The flux through the skin of the ellipsoid is equal to the integral of the Div(F) over the meat inside that skin. \[ \int _{-4}^4\int _{-\sqrt{16-x^2}}^{\sqrt{16 -x^2}}\int _{-\frac{1}{2} \sqrt{-x^2-y^2+16}}^{\frac{ 1}{2} \sqrt{-x^2-y^2+16}}(2 x+4 y+6 z)dzdydx \] Since Div(F) is odd in x, in y and in z and the region is symmetric with respect to x, y and z, the above integral is equal to zero.
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