Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²))j + (3x + 4y +6e²² (a) Find curl F. curl F - <0,0,0> (b) What does your answer to part (a) tell you about SF. dr where C' is the circle (x − 15)² + (y - 10)² = 1 in the xy-plane, oriented clockwise? ScFdr = 0 (c) If C is any closed curve, what can you say about ScF. dr? SF.dr = 0 (d) Now let C be the half circle (x − 15)² + (y — 10)² = 1 in the xy-plane with y > 10, traversed from (16, 10) to (14, 10). Find SF. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. ScF. dr =
Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²))j + (3x + 4y +6e²² (a) Find curl F. curl F - <0,0,0> (b) What does your answer to part (a) tell you about SF. dr where C' is the circle (x − 15)² + (y - 10)² = 1 in the xy-plane, oriented clockwise? ScFdr = 0 (c) If C is any closed curve, what can you say about ScF. dr? SF.dr = 0 (d) Now let C be the half circle (x − 15)² + (y — 10)² = 1 in the xy-plane with y > 10, traversed from (16, 10) to (14, 10). Find SF. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. ScF. dr =
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 understand how to find (a) using stoke's theorem and I know (b) and (c) equals 0 but I do not understand how to find (d)
Transcribed Image Text:Let
F = (3z + 3x²) ¿+ (6y + 4z + 4 sin(y²)) j + (3x + 4y + 6e²²) k
i
(a) Find curl F.
curl F
-
<0,0,0>
(b) What does your answer to part (a) tell you about
SF. dr where C is the circle
(x − 15)² + (y − 10)² = 1 in the xy-plane, oriented
clockwise?
SF-dr = 0
(c) If C is any closed curve, what can you say about
ScF · dř?
SoF. dr = 0
(d) Now let C be the half circle
(x − 15)² + (y − 10)² = 1 in the xy-plane with
y > 10, traversed from (16, 10) to (14, 10). Find
SF. dr by using your result from (c) and considering
C plus the line segment connecting the endpoints of C.
ScF. dr =
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