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Problem 36 Medium Difficulty

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 3 centered at the origin oriented counterclockwise.

Answer

$-18 \pi$
It's because $F$ is not conservative.

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Video Transcript

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