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Calculate F(r)•dr for the following data. If F is a force, this gives the work done in the displacement along C. (Show the details.) 1. F = [y, x], C the parabola y = 5x² from A: (0, 0) to B: (2, 20) %3D 2. F as in Prob. 1, C the shortest path from A to B. Is the integral smaller? Give reason. 3. F as in Prob. 1, C from A straight to (2, 0), then vertically up to B 4. F = [x2, y², 0], C the semicircle from (2, 0) to (-2, 0), y 2 0 5. F = [xy, xy], C: r [cosh t, sinh t, 0], %3D 0 stS 2. Sketch C. 6. F = [e", e"] clockwise along the circle with center (0, 0) from (1, 0) to (0, -1) %3D

Calculate F(r)•dr for the following data. If F is a force, this gives the work done in the displacement along C. (Show the details.) 1. F = [y, x], C the parabola y = 5x² from A: (0, 0) to B: (2, 20) %3D 2. F as in Prob. 1, C the shortest path from A to B. Is the integral smaller? Give reason. 3. F as in Prob. 1, C from A straight to (2, 0), then vertically up to B 4. F = [x2, y², 0], C the semicircle from (2, 0) to (-2, 0), y 2 0 5. F = [xy, xy], C: r [cosh t, sinh t, 0], %3D 0 stS 2. Sketch C. 6. F = [e", e"] clockwise along the circle with center (0, 0) from (1, 0) to (0, -1) %3D

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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PROBLEM SET 10I 1-12 LINE INTEGRAL. WORK DONE BY A FORCE Calculate F(r) dr for the following data. If F is a force, this gives the work done in the displacement along C. (Show the details.) 1. F = [y, x*], C the parabola y = 5x² from A: (0, 0) to B: (2, 20) 2. F as in Prob. 1, C the shortest path from A to B. Is the integral smaller? Give reason. 3. F as in Prob. 1, C from A straight to (2, 0), then vertically up to B 4. F = [x2, y2, 0], C the semicircle from (2, 0) to (-2, 0), у 2 0 5. F = [xy, xy], C: r [cosh t, sinh t, 0], 0 SIS 2. Sketch C. 6. F = [e", e] clockwise along the circle with center (0, 0) from (1, 0) to (0, -1) 7. F = [z, x, yl, C: r = [cos t, sin t, 1] from (1, 0, 0) to (1, 0, 4 7) 8. F = [cosh x, sinh y, e], C: r = [t. , from (0, 0, 0) to . %3D %3D 9. F as in Prob. 8, C the straight segment from (0, 0, 0) to 10. F = [x, -z, 2y] from (0, 0, 0) straight to (1, 1, 0), then to (1, 1, 1), back to (0, 0, 0)
Transcribed Image Text:PROBLEM SET 10I 1-12 LINE INTEGRAL. WORK DONE BY A FORCE Calculate F(r) dr for the following data. If F is a force, this gives the work done in the displacement along C. (Show the details.) 1. F = [y, x*], C the parabola y = 5x² from A: (0, 0) to B: (2, 20) 2. F as in Prob. 1, C the shortest path from A to B. Is the integral smaller? Give reason. 3. F as in Prob. 1, C from A straight to (2, 0), then vertically up to B 4. F = [x2, y2, 0], C the semicircle from (2, 0) to (-2, 0), у 2 0 5. F = [xy, xy], C: r [cosh t, sinh t, 0], 0 SIS 2. Sketch C. 6. F = [e", e] clockwise along the circle with center (0, 0) from (1, 0) to (0, -1) 7. F = [z, x, yl, C: r = [cos t, sin t, 1] from (1, 0, 0) to (1, 0, 4 7) 8. F = [cosh x, sinh y, e], C: r = [t. , from (0, 0, 0) to . %3D %3D 9. F as in Prob. 8, C the straight segment from (0, 0, 0) to 10. F = [x, -z, 2y] from (0, 0, 0) straight to (1, 1, 0), then to (1, 1, 1), back to (0, 0, 0)
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