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Use Green's Theorem to prove that for any positively oriented piecewise-smooth simple closed curve C, the line inte- gral fo x dy is equal to the area of the region D bounded by the curve C. Hint: use Green's Theorem with P(x, y) = 0 C and Q(x, y) = x.

Use Green's Theorem to prove that for any positively oriented piecewise-smooth simple closed curve C, the line inte- gral fo x dy is equal to the area of the region D bounded by the curve C. Hint: use Green's Theorem with P(x, y) = 0 C and Q(x, y) = x.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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11. Use Green's Theorem to prove that for any positively oriented piecewise-smooth simple closed curve C, the line inte- x dy is equal to the area of the region D bounded by the curve C. Hint: use Green's Theorem with P(x, y) = 0 and Q(x, y) = x. gral C
Transcribed Image Text:11. Use Green's Theorem to prove that for any positively oriented piecewise-smooth simple closed curve C, the line inte- x dy is equal to the area of the region D bounded by the curve C. Hint: use Green's Theorem with P(x, y) = 0 and Q(x, y) = x. gral C
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