Let C₁ be the directed line segment that starts at (2,0) and ends at (-3,-5) and C₂ be the parabola with parametrization x = =t, y = 4 – t² for t € [−3,2]. Let ♬ be the vector field F(x, y) = (x² − 4y) î + (2x + 3y²) î. (a) Evaluate ſc₂ F · dr. (b) Evaluate fF.dr where C is the positively oriented path consisting of the parabola y = 4—x² starting from (2, 0) to (−3,−5) and the line segment from (-3, −5) back to (2,0). (c) Use the results in (a) and (b) to evaluate Sc₂ F · dr.
Let C₁ be the directed line segment that starts at (2,0) and ends at (-3,-5) and C₂ be the parabola with parametrization x = =t, y = 4 – t² for t € [−3,2]. Let ♬ be the vector field F(x, y) = (x² − 4y) î + (2x + 3y²) î. (a) Evaluate ſc₂ F · dr. (b) Evaluate fF.dr where C is the positively oriented path consisting of the parabola y = 4—x² starting from (2, 0) to (−3,−5) and the line segment from (-3, −5) back to (2,0). (c) Use the results in (a) and (b) to evaluate Sc₂ F · dr.
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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![1.
Let C₁ be the directed line segment that starts at (2,0) and ends at (-3,-5) and C₂
be the parabola with parametrization x = t, y = 4 - t² for t € [−3,2]. Let F be the vector field
F(x, y) = (x² – 4y) î+ (2x + 3y²) î.
F.dr.
(a) Evaluate Sc₁
(b) Evaluate fF.dr where C is the positively oriented path consisting of the parabola y = 4-x²
starting from (2,0) to (−3,−5) and the line segment from (-3, −5) back to (2,0).
(c) Use the results in (a) and (b) to evaluate ſc₂ F · dr.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d53998f-4545-44c0-bfeb-c9570c805b86%2F3f6a8de6-f045-4e73-aa90-c59122853234%2F7x0upjs_processed.png&w=3840&q=75)
Transcribed Image Text:1.
Let C₁ be the directed line segment that starts at (2,0) and ends at (-3,-5) and C₂
be the parabola with parametrization x = t, y = 4 - t² for t € [−3,2]. Let F be the vector field
F(x, y) = (x² – 4y) î+ (2x + 3y²) î.
F.dr.
(a) Evaluate Sc₁
(b) Evaluate fF.dr where C is the positively oriented path consisting of the parabola y = 4-x²
starting from (2,0) to (−3,−5) and the line segment from (-3, −5) back to (2,0).
(c) Use the results in (a) and (b) to evaluate ſc₂ F · dr.
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