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Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by the upper semicircle C₂ of the circle x² + y² = 4x, with counterclock- wise orientation. (a) Sketch the given curve C. (b) (c) Identify parametric representations for C₁ and C₂. Show that Green's Theorem is satisfied by evaluating both the line integral and the double integral for the given vector field F and curve C.

Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by the upper semicircle C₂ of the circle x² + y² = 4x, with counterclock- wise orientation. (a) Sketch the given curve C. (b) (c) Identify parametric representations for C₁ and C₂. Show that Green's Theorem is satisfied by evaluating both the line integral and the double integral for the given vector field F and curve C.

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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Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by the upper semicircle C₂ of the circle x² + y² = 4x, with counterclock- wise orientation. (a) (b) (c) Sketch the given curve C. Identify parametric representations for C₁ and C2. Show that Green's Theorem is satisfied by evaluating both the line integral and the double integral for the given vector field F and curve C.
Transcribed Image Text:Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by the upper semicircle C₂ of the circle x² + y² = 4x, with counterclock- wise orientation. (a) (b) (c) Sketch the given curve C. Identify parametric representations for C₁ and C2. Show that Green's Theorem is satisfied by evaluating both the line integral and the double integral for the given vector field F and curve C.
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