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Consider the rotation field F = (-y,.x) and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line integral JF.T ds is independent of the path, where C is a path from (1,0) to (0,1)? с C... What is the value of the line integral for the path C₁? 1 (Type an exact answer, using as needed.) What is the value of the line integral for the path C₂, which is a quarter of the unit circle centered at the origin? (Type an exact answer, using as needed.) (0, 1) C₂ C₁ C₂ (1,0) x

Consider the rotation field F = (-y,.x) and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line integral JF.T ds is independent of the path, where C is a path from (1,0) to (0,1)? с C... What is the value of the line integral for the path C₁? 1 (Type an exact answer, using as needed.) What is the value of the line integral for the path C₂, which is a quarter of the unit circle centered at the origin? (Type an exact answer, using as needed.) (0, 1) C₂ C₁ C₂ (1,0) x

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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I found the value for path C1, I need help finding the value for the path C2 and C3.

Consider the rotation field F = (y,x) and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line integral F. T ds is independent of the path, where C is a path from (1,0) to (0,1)? What is the value of the line integral for the path C₁? 1 (Type an exact answer, using as needed.) What is the value of the line integral for the path C₂, which is a quarter of the unit circle centered at the origin? (Type an exact answer, using í as needed.) (0, 1) 1² C3 (1,0) x
Transcribed Image Text:Consider the rotation field F = (y,x) and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line integral F. T ds is independent of the path, where C is a path from (1,0) to (0,1)? What is the value of the line integral for the path C₁? 1 (Type an exact answer, using as needed.) What is the value of the line integral for the path C₂, which is a quarter of the unit circle centered at the origin? (Type an exact answer, using í as needed.) (0, 1) 1² C3 (1,0) x
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