Consider the vector field vec$(F)=($:$x^3{y}^4,x^4{y}^3$:$).$

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 plecewtse smooth curve $(C)$ from $(-5,3)$ to $(0,-2).$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=q,$