Suppose $\nabla f (x,y) = 2 y \sin(xy) \vec{i} + 2 x \sin(xy)\vec{j}$, $\vec{F} = \nabla f(x,y)$, and $C$ is the segment of the parabola $y = 3 x^2$ from the point $(2,12)$ to $(6,108)$. Then

$\displaystyle \int_C \vec{F} \cdot d\vec{r}$ =