Find the circulation done by the velocity field V(x, y)= -y/[(x+1)^2 +4y^2]i + (x+1)/[(x+1)^2 +4y^2]j around the positively oriented square with vertices (2, 0), (0, 2), (−2, 0), and (0, −2).

The circulation of V around the given path (call it C) is simply the line integral of V along C. Since C is a closed curve, we can use Green's theorem.

where int(C) is the interior or region bounded by C.

We have

so the double integral and hence the circulation is zero.

your answer is a

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congruent segments

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