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Let R be the annulus defined by {1 ≤ x² + y² ≤ 4} and let C₁ and C₂ be the circles of ratius 2 and 1 respectively around the origin, oriented counterclockwise. (-y, 2x). Show by direct calculation that Let F = fc, FoT ds-fc₂F o T ds = f curl F dA.

Let R be the annulus defined by {1 ≤ x² + y² ≤ 4} and let C₁ and C₂ be the circles of ratius 2 and 1 respectively around the origin, oriented counterclockwise. (-y, 2x). Show by direct calculation that Let F = fc, FoT ds-fc₂F o T ds = f curl F dA.

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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3. Let R be the annulus defined by {1 ≤ x² + y² ≤ 4} and let C₁ and C₂ be the circles of ratius 2 and counterclockwise. Let F = 1 respectively around the origin, oriented -y, 2x). Show by direct calculation that SSR curl F dA. = fc, FoT ds-fc₂ FoT ds
Transcribed Image Text:3. Let R be the annulus defined by {1 ≤ x² + y² ≤ 4} and let C₁ and C₂ be the circles of ratius 2 and counterclockwise. Let F = 1 respectively around the origin, oriented -y, 2x). Show by direct calculation that SSR curl F dA. = fc, FoT ds-fc₂ FoT ds
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