Evaluate

$$ C

$($y $+8$ sin$($x$))$ dx $+($z$2+5$ cos$($y$))$ dy $+$ x$3$ dz

where C is the curve

r$($t$)=$

sin$($t$),$ cos$($t$),$ sin$(2$t$)$

$,0$ t $2.$

$($Hint: Observe that C lies on the surface z $=2$xy$.)$

$$ C

F $$ dr $=$