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Multivariable Calculus

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Green's Theorem

MVCALC-U4XX6A

Let $\vec{F}$ be a vector field in the plane. What does Green's Theorem say about $\vec{F}$?

A

The circulation of $\vec{F}$ about the boundary of a reigon $R$ is equal to the $\oint_{\partial R} \vec{F} \cdot d\vec{s}$.

B

The circulation of $\vec{F}$ about the boundary of a region $R$ is equal to the area of $R$.

C

The circulation of $\vec{F}$ about the boundary of a region $R$ is equal to $\iint_R \left( \frac{\partial F_2}{\partial x} - \frac{\partial F_1}{\partial y} \right) dA$.

D

The circulation of $\vec{F}$ about the boundary of a region $R$ is equal to $\iint_R \left( \frac{\partial F_1}{\partial x} - \frac{\partial F_2}{\partial y} \right) dA$.

E

None of the Above