Consider the vector field $\vec{F} = \langle 3x + 4y, 4x + 5y \rangle$.
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
$f(x, y) = \text{________}$
If $\vec{F}$ is conservative, use $f(x, y)$ to evaluate $\int_C \vec{F} \cdot d\vec{r}$ along a piecewise smooth curve $(C)$ from
$(2, -4)$ to $(5, -1)$.
$\int_C \vec{F} \cdot d\vec{r} = \text{________}$
