(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use Green’s theorem to find the integral

[itex]\oint_{\gamma} \frac{-y}{x^2+y^2}dx+\frac{x}{x^2+y^2}dy[/itex]

along two different curves γ: first where γ is the simple closed curve which goes along x = −y2 + 4 and x = 2, and second where γ is the square with vertices (−1, 0), (1, 0), (0, 1), (0, −1).

2. Relevant equations

3. The attempt at a solution

I'm bit confused b/c

[itex]d(\frac{-y}{x^2+y^2})/dy = \frac{y^2-x^2}{(x^2+y^2)^2}[/itex]

[itex]d(\frac{x}{x^2+y^2})/dx = \frac{y^2-x^2}{(x^2+y^2)^2}[/itex]

Then by Green's theorem one gets

[itex]\int_{A}\int (d(\frac{x}{x^2+y^2})/dx-d(\frac{-y}{x^2+y^2})/dy) dx dy = \int_{A}\int 0 dx dy = 0[/itex]

What am I missing?

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# Solve using Green's Theorem

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