$1,$ Let $F=($:$2xy+z^2,x^2,2xz$:$)$ and let $C$ be the circle $r(t)=($:$6sint,2cost,4sint$:$),$ for $0t2.$ Evaluate $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*$ dr using any method.

$o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr=q,($Simplify your answer.$)$