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Evaluate $\oint_{C} \mathbf{F} \cdot d \mathbf{r}$ for the following vector fields and closed oriented curves $C$ by parameterizing $C .$ If the integral is not zero, give an explanation.

$\mathbf{F}=\langle y, x\rangle ; C$ is the circle of radius 8 centered at the origin oriented counterclockwise.

$$0$$

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