Let C₁ be the directed line segment that starts at (2,0) and ends at (−3,−5) and C₂be the parabola with parametrization x = t, y = 4 — t² for t € [−3, 2]. Let F be the vector fieldF(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-x²starting 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.

Answered: Image /qna-images/answer/e7a18201-61ef-4f6f-8191-49c0c7d64bcd.jpg

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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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