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Using Green's Theorem similarly to as in the proof of a version of the Cauchy-Goursat Theorem from class (and the text), show that if C is a simple closed curve, oriented counterclockwise, then the area enclosed by C is given by 1 L z dz 2i C

Using Green's Theorem similarly to as in the proof of a version of the Cauchy-Goursat Theorem from class (and the text), show that if C is a simple closed curve, oriented counterclockwise, then the area enclosed by C is given by 1 L z dz 2i C

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using Green's Theorem similarly to as in the proof of a version of the Cauchy-Goursat Theorem from class (and the text), show that if \( C \) is a simple closed curve, oriented counterclockwise, then the area enclosed by \( C \) is given by \[ \frac{1}{2i} \oint_{C} \overline{z} \, dz \]
Transcribed Image Text:Using Green's Theorem similarly to as in the proof of a version of the Cauchy-Goursat Theorem from class (and the text), show that if \( C \) is a simple closed curve, oriented counterclockwise, then the area enclosed by \( C \) is given by \[ \frac{1}{2i} \oint_{C} \overline{z} \, dz \]
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