vec$(F)=6$yvec$(i)-6$xvec$(j)$ and $C$ is the boundary of $S,$ the part of the surface $z=4-x^2-y^2$ above the $xy-$plane, oriented upward.

Calculate the circulation, ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ in two ways, directly and using

Stokes' Theorem.

NOTE: Enter the exact answers, or round to three decimal places.

Calculated directly: ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$

Using Stokes' Theorem: ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$