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.
Complex Line Integral
2
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complex-analysis