Well, I hope this is a stokes problem. Im honestly a bit lost on this so please help me out!
Suppose I have a simple closed curve, C, in the plane w/ counterclockwise direction. I need to calculate $\int_C F\bullet dr$ in terms of the area inside the curve. With $F=\frac x2j$.
$$\int_C F\bullet dr=\int_Scurl\vec F\bullet D\vec A$$
I calculated $curl\vec F$ to be: $$\nabla \times\vec F= \frac 12\vec k$$
How do I find $D\vec A$?