4. Let F(x, y, z)=(2², 2+y, 3r). Let C be a curve in R³. Which of the following is a correct statement? -√2² dz [Fds. • [ ²² dx + f (x + y) dy + | : (d) More than one of the other choices. (a) √ 2² ds = (b) L.F F.dr= (e) F. dr = + [ 2² dy + √ 2² dz. x + [ 3a dz.
4. Let F(x, y, z)=(2², 2+y, 3r). Let C be a curve in R³. Which of the following is a correct statement? -√2² dz [Fds. • [ ²² dx + f (x + y) dy + | : (d) More than one of the other choices. (a) √ 2² ds = (b) L.F F.dr= (e) F. dr = + [ 2² dy + √ 2² dz. x + [ 3a dz.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
explain 4
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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