I was given the following question:
Compute the work done by the force field $\mathbf{F}\left(x,y\right)=<2y,-2x>$ along the curve C, where C is the line segment from $\left(4,2\right)$ to $\left(0,4\right)$.
I know that $W=\int_{C}\ F\left(x,y,z\right)\ dr=\int_{C}2ydx-2xdy$.
My question is - how do I create a parametric equation for $x$ and $y$? I think I need to make one in order to find my limits and substitute it in , I just don't know how.
Hint: You can always parameterize a line segment from point $P_1$ to $P_2$ as $$P_1 + (P_2 - P_1) t, ~ 0 \leq t \leq 1$$