(Solved):   Use the Divergence Theorem to compute the net outward flux of the following field across t ...

 

Use the Divergence Theorem to compute the net outward flux of the following field across the given surface S. \[ F=\left\{-5 y+x,-6 x^{2}-3 y,-y-3 z\right\rangle \] \( S \) is the sphere \( \left\{(x, y, z): x^{2}+y^{2}+z^{2}=9\right\} \) The net outward flux across the surface is (Type an exact answer, using \( \pi \) as needed.)