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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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ANN 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:ANN 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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