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(c) Suppose D is enclosed by C₁, C₂ and C3. Use Green's Theorem to evaluate the line integral F. dr.

(c) Suppose D is enclosed by C₁, C₂ and C3. Use Green's Theorem to evaluate the line integral F. dr.

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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please help with part c

 

Question 5 Define the vector field F by F = (x²-y)i + (x - xy)j. Let C be the curve consisting of C₁, C₂ and C3 as shown in the following Figure Q5. C₁ is a line from A(0,0) to B(0,1), C₂ is a quarter circle with the parameter equation r(t) = cos ti + sin tj (π/2 < t < π). C3 is a line from C(-1,0) to A(0,0). (a) (b) (c) C2 C = (-1,0) D Find the curl of F. -0.5 C3 1:5 05|C1 O B = (0, 1) -0.5 A = (0,0) 0.5 Figure Q5 Sc₂² Compute the line integral of F along C₁, C₂, C3, F. dr. F. dr and dr. F. Suppose D is enclosed by C₁, C₂ and C3. Use Green's Theorem to evaluate the line integral fF.dr.
Transcribed Image Text:Question 5 Define the vector field F by F = (x²-y)i + (x - xy)j. Let C be the curve consisting of C₁, C₂ and C3 as shown in the following Figure Q5. C₁ is a line from A(0,0) to B(0,1), C₂ is a quarter circle with the parameter equation r(t) = cos ti + sin tj (π/2 < t < π). C3 is a line from C(-1,0) to A(0,0). (a) (b) (c) C2 C = (-1,0) D Find the curl of F. -0.5 C3 1:5 05|C1 O B = (0, 1) -0.5 A = (0,0) 0.5 Figure Q5 Sc₂² Compute the line integral of F along C₁, C₂, C3, F. dr. F. dr and dr. F. Suppose D is enclosed by C₁, C₂ and C3. Use Green's Theorem to evaluate the line integral fF.dr.
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