Given vec$($F$)=($y$^(2)$z$^(3),2$xyz$^(3),3$xy$^(2)$z$^(2)).$

$($a$)$ Is vec$($F$)$ conservative? Why?

$($b$)$ If your answer is yes, find a potential function f$($x$,$y$,$z$)$ such that gradf$=$vec$($F$).$

$($c$)$ Evaluate the line integral $\backslash$int$\_$c vec$($F$)*$vec$($dr$),$ where c is the helix $(4$cost$,2$sint$,$t$)$ from t$=4\backslash$pi to

t$=(\backslash$pi $)/(2).$