$In$ Exercises $5-10,$ calculate curl$(F)$ and then apply Stokes$$ Theorem

$to$ compute the flux $of$ curl$(F)$ through the given surface using a line

integral.

$F=($:$2y,e^z,-arctanx$:$),$ that part $of$ the paraboloid $z=4-$

$x^2-y^2$ cut off $by$ the $xy-$plane with upward$-$pointing unit normal vec$-$

tor