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Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (−1, −1) to (0, 0), C₂ is the line segment from (0, 0) to (-1, 1), and C3 is the portion of the circle x² + y² = 2 from (-1, 1) to (−1, −1) traced counterclockwise. Use Green's Theorem to set up an iterated double integral equal to § (−y³ + x)dx + (x³ + x² )dy.

Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (−1, −1) to (0, 0), C₂ is the line segment from (0, 0) to (-1, 1), and C3 is the portion of the circle x² + y² = 2 from (-1, 1) to (−1, −1) traced counterclockwise. Use Green's Theorem to set up an iterated double integral equal to § (−y³ + x)dx + (x³ + x² )dy.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.4: Analytic Proofs
Problem 28E
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Using Green's Theorem, answer: 

 

Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment from (0, 0) to (−1, 1), and C3 is the portion of the circle x² + y² = 2 from (-1, 1) to (-1, −1) traced counterclockwise. Use Green's Theorem to set up an iterated double integral equal to § (−y³ + x)dx + (x³ + x² )dy.
Transcribed Image Text:Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment from (0, 0) to (−1, 1), and C3 is the portion of the circle x² + y² = 2 from (-1, 1) to (-1, −1) traced counterclockwise. Use Green's Theorem to set up an iterated double integral equal to § (−y³ + x)dx + (x³ + x² )dy.
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