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    Proving the Area Enclosed by a Simple Closed Path using Complex Analysis

    Thank you sir! Solved! Not sure how to update thread title.
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    Proving the Area Enclosed by a Simple Closed Path using Complex Analysis

    Thank you again for the assistance. I have almost gotten to the conclusion that I need but I'm not sure how to proceed. I have shown that: (1/2)\int_{0}^{1} \bar{z}dz = (1/2)\int_{0}^{1} x(t)y'(t)dt-y(t)x'(t)dt + (1/2i)\int_{0}^{1} x(t)x'(t)dt-y(t)y'(t)dt I am assuming that the integral...
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    Proving the Area Enclosed by a Simple Closed Path using Complex Analysis

    thank you very much for your help.
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    Proving the Area Enclosed by a Simple Closed Path using Complex Analysis

    Homework Statement C = positively oriented simple closed piecewise smooth path Prove that: (1/2i)*\int_{C}\bar{z}dz is the area enclosed by C. Homework Equations *I know that the curve C is piecewise smooth so that it can be broken up into finitely many pieces so that each piece...
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