The figure below open cylindrical can, $S$, standing on the $xy$-plane. ($S$ has a bottom and sides, but no top.)

The side of $S$ is given by $x^2 + y^2 = 1$, and its height is 4.

(a) Give a parametric equation, $\vec r(t)$ for the rim, $C$.
$\vec r(t) =$ , with $\le t\le$ .
(For this problem, enter your vector equation with angle-bracket notation: $<f(t), g(t), h(t)>$.)

(b) If $S$ is oriented outward and downward, find $\int_S\mbox{curl }(-2 y\vec i+ 2 x\vec j+ 6 z\vec k)\cdot d\vec A$.
$\int_S\mbox{curl }(-2 y\vec i+ 2 x\vec j+ 6 z\vec k)\cdot d\vec A =$