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7. So -y dx + x dy x² + y² G₁₁: x² + y² = 1 C₁ traversed in a clockwise direction. (b) Green's theorem cannot be used directly to evaluate So -y dx + x dy x² + y² where C₂ is given by C₂ the parabola y² = x+2 traversed counterclockwise from (2,2) to (2,-2), and then along the vertical line segment from (2,-2) to (2,2). Show how the result of part(a) can be used with Green's theorem to evaluate the above line integral. (a) Evaluate

7. So -y dx + x dy x² + y² G₁₁: x² + y² = 1 C₁ traversed in a clockwise direction. (b) Green's theorem cannot be used directly to evaluate So -y dx + x dy x² + y² where C₂ is given by C₂ the parabola y² = x+2 traversed counterclockwise from (2,2) to (2,-2), and then along the vertical line segment from (2,-2) to (2,2). Show how the result of part(a) can be used with Green's theorem to evaluate the above line integral. (a) Evaluate

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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7. - -y dx + x dy S C₁: x² + y² = 1 C₁ x² + y² traversed in a clockwise direction. (b) Green's theorem cannot be used directly to evaluate S -y dx + x dy C₂ x² + y² where C₂ is given by the parabola y² = x+2 traversed counterclockwise from (2,2) to (2,-2), and then along the vertical line segment from (2,-2) to (2,2). Show how the result of part(a) can be used with Green's theorem to evaluate the above line integral. (a) Evaluate
Transcribed Image Text:7. - -y dx + x dy S C₁: x² + y² = 1 C₁ x² + y² traversed in a clockwise direction. (b) Green's theorem cannot be used directly to evaluate S -y dx + x dy C₂ x² + y² where C₂ is given by the parabola y² = x+2 traversed counterclockwise from (2,2) to (2,-2), and then along the vertical line segment from (2,-2) to (2,2). Show how the result of part(a) can be used with Green's theorem to evaluate the above line integral. (a) Evaluate
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