Consider the vector field vec$(F)=($:$3x+4y,4x+5y$:$).$

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 $(2,-4)$ to $(5,-1).$

$({\displaystyle \underset{C}{\overset{(2)}{}}},-4$vec$(F)*dvec(r)=$

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