Let $D$ be the half$-$annulus given by $\{(r,)|2r4,0\},$ and let vec$(F)=($:$7y^2,-8x^2$:$),$ with the boundary curve $C$ of the region oriented counterclockwise. Use Green's theorems to compute the following.

$($a$)$ the circulation of vec$(F)$ around $C$

$$

$($b$)$ the flux of the vector field vec$(F)$ outward from the region $D$