Use Green's Theorem to calculate the work done by the given force field $\vec{F}$ in moving a particle counterclockwise once around the indicated curve $C$.
$\vec{F} = 5x^2y^3\vec{i} + 7x^3y^2 \vec{j}$, $C$ is the triangle with vertices $(0,0),(3,0),(0,6).$
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Because it is indicated that the particle is moved counterclockwise, I assumed that I should multiply the answer by $-1$, as Green's Theorem uses a positive orientation. However, upon setting up and solving the integral, I actually get the negative of the correct answer, indicating that my decision to take the negative was incorrect. But how can this be? If Green's Theorem is based around positive orientation and I'm dealing with negative, shouldn't that mean that I must take the negative of the integral?