Let C₁ be the directed line segment that starts at (2,0) and ends at (-3,-5) and C₂ ɔe 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 §♂ Ē·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 ɔe 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 §♂ Ē·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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![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) ĵ.
(a) Evaluate Sc₁ F· dr.
F.
(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%2F5daccb78-2e97-407d-8a2f-780b21ee96a4%2Fe7a18201-61ef-4f6f-8191-49c0c7d64bcd%2F81jyg1_processed.png&w=3840&q=75)
Transcribed Image Text: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) ĵ.
(a) Evaluate Sc₁ F· dr.
F.
(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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