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6. F = (2,2, x) is a conservative vector field (a) Determine the potential o where Vo = F. (b) Let C₁ be the curve parametrized by Fi(t) (5t, 2 t, t²), for 0 ≤ t ≤ 2. Use the fundamental theorem of line integrals to evaluate the work required to move an object in the force field along the curve C₁ from (0, 2, 0) to (10, 0, 4). (c) Let C₂ be the simple closed curve parametrized by T2(t) 0≤t≤ 27. Evaluate fF.dr. = (2 sin t, 2 cos t, cost sin t), for

6. F = (2,2, x) is a conservative vector field (a) Determine the potential o where Vo = F. (b) Let C₁ be the curve parametrized by Fi(t) (5t, 2 t, t²), for 0 ≤ t ≤ 2. Use the fundamental theorem of line integrals to evaluate the work required to move an object in the force field along the curve C₁ from (0, 2, 0) to (10, 0, 4). (c) Let C₂ be the simple closed curve parametrized by T2(t) 0≤t≤ 27. Evaluate fF.dr. = (2 sin t, 2 cos t, cost sin t), for

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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6. F = (2,2, x) is a conservative vector field (a) Determine the potential o where Vo = F. (b) Let C₁ be the curve parametrized by Fi(t) (5t, 2 t, t²), for 0 ≤ t ≤ 2. Use the fundamental theorem of line integrals to evaluate the work required to move an object in the force field along the curve C₁ from (0, 2, 0) to (10, 0, 4). (c) Let C₂ be the simple closed curve parametrized by r2(t) 0≤t≤ 27. Evaluate fF.dr. = (2 sin t, 2 cos t, cost sin t), for
Transcribed Image Text:6. F = (2,2, x) is a conservative vector field (a) Determine the potential o where Vo = F. (b) Let C₁ be the curve parametrized by Fi(t) (5t, 2 t, t²), for 0 ≤ t ≤ 2. Use the fundamental theorem of line integrals to evaluate the work required to move an object in the force field along the curve C₁ from (0, 2, 0) to (10, 0, 4). (c) Let C₂ be the simple closed curve parametrized by r2(t) 0≤t≤ 27. Evaluate fF.dr. = (2 sin t, 2 cos t, cost sin t), for
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