(0,3) C1:x² + y² = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y?i + (3xy + 4x)j, answer the following questions. a) Determine whether the following statements are True (T) False (F). Steps T/F i The r(t) for the equation Ci is r(t) = 3 cos t i + 3 sin t j. ii Then, r'(t) = 3 sin t i – 3 cos tj. F iii Based on (i), the S, P dx + Q dy can be simplified as, S-27 sin30 + 54 cos20 sin 0 + 36 cos e de F iv The limit of integration the S, P dx + Q dy is F f de V The equation of the curve C, is y = 0. vi By parametrizing the equation C2, the P dx + Q dy can be simplified as, Se 3t dt F vii The limit of integration for the S, P dx + Q dy is T b) Use Green's theorem to calculate the work performed by the given vector F that moves around the curve C as shown in the Figure 1. (ans: 18+ 187)
(0,3) C1:x² + y² = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y?i + (3xy + 4x)j, answer the following questions. a) Determine whether the following statements are True (T) False (F). Steps T/F i The r(t) for the equation Ci is r(t) = 3 cos t i + 3 sin t j. ii Then, r'(t) = 3 sin t i – 3 cos tj. F iii Based on (i), the S, P dx + Q dy can be simplified as, S-27 sin30 + 54 cos20 sin 0 + 36 cos e de F iv The limit of integration the S, P dx + Q dy is F f de V The equation of the curve C, is y = 0. vi By parametrizing the equation C2, the P dx + Q dy can be simplified as, Se 3t dt F vii The limit of integration for the S, P dx + Q dy is T b) Use Green's theorem to calculate the work performed by the given vector F that moves around the curve C as shown in the Figure 1. (ans: 18+ 187)
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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Transcribed Image Text:(0,3)
C1:x² + y² = 9.
(-3,0)
C2
(3,0)
Figure 1
Based on Figure 1 and given that F = y² i + (3xy + 4x)j, answer the following questions.
a) Determine whether the following statements are True (T) or False (F).
Steps
T/F
i
The r(t) for the equation C1 is r(t) = 3 cos t i + 3 sin t j.
T
ii
Then, r'(t) = 3 sin t i – 3 cos t j.
F
iii
Based on (i), the S, P dx + Q dy can be simplified as,
S-27 sin30 + 54 cos?0 sin 0 + 36 cos 0 de
F
iv
The limit of integration the f. P dx + Q dy is
F
f d0
The equation of the curve C2 is y= 0.
vi
By parametrizing the equation C2, the S, P dx + Q dy can be simplified as,
Sc 3t dt
vii The limit of integration for the P dx + Q dy is
f de
b) Use Green's theorem to calculate the work performed by the given vector F that moves
around the curve C as shown in the Figure 1. (ans: 18+ 187)
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