vec$(F)=8$xyvec$(i)+8$yzvec$(j)+8$xzvec$(k)$ and $C$ is the boundary of $S,$ the part of the surface $z=1-x^2$ for $0x1$ and $-2y2,$ oriented upward. Calculate the circulation, ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ in two ways, directly and using Stokes' Theorem.

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

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