Consider the vector field vec$(F)=($:$4xy7y-8,2x^{2}7x$:$).$

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 $(-3,3)$ to $(-2,-5).$

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

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