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Use a graph of the vector field $\mathbf{F}$ and the curve $C$ to guess whether the line integral of $\mathbf{F}$ over $C$ is positive, negative, or zero. Then evaluate the line integral.

$$\mathbf{F}(x, y)=(x-y) \mathbf{i}+x y \mathbf{j}$$ $C$ is the arc of the circle $x^{2}+y^{2}=4$ traversed counter clockwise from $(2,0)$ to $(0,-2)$

Line Integral is $3 \pi+\frac{2}{3}$

Vector Calculus

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