Consider the vector field vec$(F)=($:$x^2{y}^3,x^3{y}^2$:$).$

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 ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ along a piecewise smooth curve $(C)$ from $(3,4)$ to $(-3,0).{\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$