2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment from (2, 1) to (-1, 1), followed by the piece of y = a? from (-1, 1) to (0,0). Also, let F =(-1,2*y?). a) Find F-Ť ds by integrating F over each piece of C and adding the results. b) Find F.Ť ds by first converting it to a double integral using Greene's Theorem.
2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment from (2, 1) to (-1, 1), followed by the piece of y = a? from (-1, 1) to (0,0). Also, let F =(-1,2*y?). a) Find F-Ť ds by integrating F over each piece of C and adding the results. b) Find F.Ť ds by first converting it to a double integral using Greene's Theorem.
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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Transcribed Image Text:2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment from
(2, 1) to (-1,1), followed by the piece of y = x² from (-1,1) to (0,0). Also, let F = (-1,2y?).
a) Find F-Ťds
F-Ť ds by integrating F over each piece of C and adding the results.
b) Find
F.Ť ds by first converting it to a double integral using Greene's Theorem.
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