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Consider the two-dimensional vector field F⃗(x, y) = x î + y ĵ, where î and ĵ denote the unit vectors along the x-axis and the y-axis, respectively. A contour C in the x-y plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral ∮C F⃗(x, y) ⋅ (dx î + dy ĵ) is _______
Correct : 8 + 2π
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