Use the extended divergence theorem $to$ compute the total flux $of$ the vector field

vec$(F)(x,y,z)=($:$-4x^2+3xz-y,3y^3-6y,9x^2+4z^2-3x$:$)$

outward from the region $F$ that lies inside the sphere $x^2+y^2+z^2=25$ and outside the solid cylinder $x^2+y^2=4$ with top $at$

$z=1$ and bottom $atz=-1.$