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c) Compute fF.dr directly for the following. i) F(x, y) = (-y, x + 4), r(t) = (cost, sint), 0≤ t ≤2m. (Ans:2) ii) F(x, y) = (x², y), C is the portion of the parabola y = 4-², -1 < x≤2 oriented from left to right. (Ans: -2/3) iii) Compute the work done by F = (y, -z) on the portion of the parabola x = 1 - y²,0 ≤ y ≤ 1 oriented bottom to top. (Ans:-4/3) iv) Compute the work done by F = (4y, -42) around the circle of radius 2 traversed twice in the clockwise direction. (and:647)

c) Compute fF.dr directly for the following. i) F(x, y) = (-y, x + 4), r(t) = (cost, sint), 0≤ t ≤2m. (Ans:2) ii) F(x, y) = (x², y), C is the portion of the parabola y = 4-², -1 < x≤2 oriented from left to right. (Ans: -2/3) iii) Compute the work done by F = (y, -z) on the portion of the parabola x = 1 - y²,0 ≤ y ≤ 1 oriented bottom to top. (Ans:-4/3) iv) Compute the work done by F = (4y, -42) around the circle of radius 2 traversed twice in the clockwise direction. (and:647)

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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c) Compute fF.dr directly for the following. i) F(x, y) = (-y, x + 4), r(t) = (cost, sint), 0≤ t ≤2m. (Ans:2) ii) F(x, y) = (x², y), C is the portion of the parabola y = 4-², -1 < x≤2 oriented from left to right. (Ans: -2/3) iii) Compute the work done by F = (y, -z) on the portion of the parabola x = 1 - y²,0 ≤ y ≤ 1 oriented bottom to top. (Ans:-4/3) iv) Compute the work done by F = (4y, -42) around the circle of radius 2 traversed twice in the clockwise direction. (and:647)
Transcribed Image Text:c) Compute fF.dr directly for the following. i) F(x, y) = (-y, x + 4), r(t) = (cost, sint), 0≤ t ≤2m. (Ans:2) ii) F(x, y) = (x², y), C is the portion of the parabola y = 4-², -1 < x≤2 oriented from left to right. (Ans: -2/3) iii) Compute the work done by F = (y, -z) on the portion of the parabola x = 1 - y²,0 ≤ y ≤ 1 oriented bottom to top. (Ans:-4/3) iv) Compute the work done by F = (4y, -42) around the circle of radius 2 traversed twice in the clockwise direction. (and:647)
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