$(1$ point$)$ Let S be an opened cylindrical can standing on the xyS has a bottom and sides, but no top.S is given by x$^(2)+$y$^(2)=4,$ and its

height is $2.$

$($a$)$ Give a parametric equation, vec$($r$)($t$)$ for the rim, C$.$

vec$($r$)($t$)=$

$,$ with

tS is oriented outward and downward, find $\backslash$int$\_$S $($grad$\backslash$times $(-7$yvec$($i$)+7$xvec$($j$)+7$zvec$($k$)))*$dvec$($A$).$

$\backslash$int$\_$S $($grad$\backslash$times $(-7$yvec$($i$)+7$xvec$($j$)+7$zvec$($k$)))*$dvec$($A$)=$