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Let F = (3z + 3x²) i + (6y + 4z +4 sin(y²)) 3j + (3x + 4y + 6e²²) K (a) Find curl F. curl F = 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? SoF. dr = 0 (c) If C is any closed curve, what can you say about ScF. dr? ScF. dr = 0

Let F = (3z + 3x²) i + (6y + 4z +4 sin(y²)) 3j + (3x + 4y + 6e²²) K (a) Find curl F. curl F = 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? SoF. dr = 0 (c) If C is any closed curve, what can you say about ScF. dr? ScF. dr = 0

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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Let F = (3z + 3x²) i+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F = 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? SoF. dr = 0 (c) If C is any closed curve, what can you say about La F. 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 = 0
Transcribed Image Text:Let F = (3z + 3x²) i+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F = 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? SoF. dr = 0 (c) If C is any closed curve, what can you say about La F. 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 = 0
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