Indicate which of the following vector fields possess this property: For every simple closed curve (C), (oint_{C}

Question:

Indicate which of the following vector fields possess this property: For every simple closed curve $C$,

$\oint_{C} \mathbf{F} \cdot d \mathbf{r}$ is equal to the area enclosed by $C$.

(a) $\mathbf{F}(x, y)=\langle-y, 0angle$

(b) $\mathbf{F}(x, y)=\langle x, yangle$

(c) $\mathbf{F}(x, y)=\left\langle\sin \left(x^{2}ight), x+e^{y^{2}}ightangle$

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