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5. True or False? The work done by a force field F on an object moving along a path C is F. dr. (a) True. (b) False.

5. True or False? The work done by a force field F on an object moving along a path C is F. dr. (a) True. (b) False.

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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i dont understand 5 and 6

3. Let F(x, y) (3y, 2x + 2) and let C be the top half of the unit circle, beginning at (1,0) and ending at (-1,0). Which of the following is a correct simplified setup of the line integral of F over C? (a) (-3 sin²t+2 cos²t+2 cost) dt. (b) f (5 sint cost + 2 sin t) dt. (d) (3 sint, 2 cost + 2) dt. (c) Odt (e) None of the other choices. 4. Let F(x, y, z) = (22,x+y, 3x). Let C be a curve in R³. Which of the following is a correct statement? a) [ 2² ds = [ ² F.dr = (c) F F.dr= C is 2² dr + 1² F. dr. + √√ ²² dy +¸ + √2²0 2² dz. F ds. · [ ²² dx + f (x + y) dy + + [ 3a dz. (d) More than one of the other choices. (e) None of the other choices. 5. True or False? The work done by a force field F on an object moving along a path [₁ (a) True. (b) False.
Transcribed Image Text:3. Let F(x, y) (3y, 2x + 2) and let C be the top half of the unit circle, beginning at (1,0) and ending at (-1,0). Which of the following is a correct simplified setup of the line integral of F over C? (a) (-3 sin²t+2 cos²t+2 cost) dt. (b) f (5 sint cost + 2 sin t) dt. (d) (3 sint, 2 cost + 2) dt. (c) Odt (e) None of the other choices. 4. Let F(x, y, z) = (22,x+y, 3x). Let C be a curve in R³. Which of the following is a correct statement? a) [ 2² ds = [ ² F.dr = (c) F F.dr= C is 2² dr + 1² F. dr. + √√ ²² dy +¸ + √2²0 2² dz. F ds. · [ ²² dx + f (x + y) dy + + [ 3a dz. (d) More than one of the other choices. (e) None of the other choices. 5. True or False? The work done by a force field F on an object moving along a path [₁ (a) True. (b) False.
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