Consider the vector field vec$($F$)=($:$7$x$+3$y$,3$x$+6$y:$).$

The vector field is not conservative

The vector field is conservative, and the potential function such that f$(0,0)=0$ for vec$($F$)$ is

f$($x$,$y$)=$

If vec$($F$)$ is conservative, use f$($x$,$y$)$ to evaluate $\backslash$int$\_$C vec$($F$)*$dvec$($r$)$ along a piecewise smooth curve $($C$)$ from

$(3,-4)$ to $(2,4).$

$\backslash$int$\_$C vec$($F$)*$dvec$($r$)=$