Let where C is the ellipse oriented counterclockwise. The value of I is which of the following?

Question

Let  where C is the ellipse  oriented counterclockwise. The value of I is which of the following?

Quizplus · Accepted Answer

Green's theorem tells us that the value of the line integral of a vector field around a closed curve is equal to the double integral of the curl of the vector field over the region enclosed by the curve. In this case, let F(x,y) = ye^(xy)i + xe^(xy)j, then curl F = 0. Therefore, the value of the line integral is 0, and the only choice that represents 0 is (B).

Let Where C Is the Ellipse Oriented Counterclockwise