Let $\mathbf{F} = (3 xy, 6 y^2)$ be a vector field in the plane, and $C$ the path $y = 3 x^2$ joining (0,0) to (1,3) in the plane.

A. Evaluate $\int_C \mathbf{F}\cdot d\mathbf{r}$

B. Does the integral in part (A) depend on the path joining (0,0) to (1,3)? (y/n)