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Homework 8: Problem 1
(1 point)
Use Green's Theorem to find the counterclockwise circulation of the vector field $\mathbf{F} = \langle 3xy, 5x + 2y \rangle$ along the curve $C$, where $C$ is the triangle with vertices $(0,0)$, $(2,0)$, and $(0,2)$.
To do this, you must first compute the scalar curl of $\mathbf{F}$.
a) Scalar curl: $\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = $
b) Now, using your result from part (a), compute the circulation.
(Enter your answer as an exact fraction.)
Circulation = $\oint_C \mathbf{F} \cdot d\mathbf{r} = $