vec$($F$)=2$xyvec$($i$)+2$yzvec$($j$)+2$xzvec$($k$)$ and C is the boundary of S$,$ the part

of the surface z$=1-$x$^(2)$ for x and y oriented

upward. Calculate the circulation, $\backslash$int$\_$C vec$($F$)*$dvec$($r$)$ in two ways, directly

and using Stokes' Theorem.

Calculated directly: $\backslash$int$\_$C vec$($F$)*$dvec$($r$)=$

Using Stokes' Theorem: $\backslash$int$\_$C vec$($F$)*$dvec$($r$)=$