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Prove that if a differentiable curve $g:[0,1] \to \mathbb{C}$ (complex plane) parametrizes counterclockwise the boundary of an open set $O$ in $\mathbb{C}$, then under suitable conditions area of $O$ is $ {1 \over 2i } \int_g \overline{z} dz $ computed over the boundary.

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Write your contour integral out explicitly using the parameterization $g(t)$ and then use Green's theorem.

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    oh! u r a savior! i can be so silly sometimes :-) thanks a lot!2011-01-23