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Let F = (2x + 2x²) 7+ (7y+7z+ 7 sin(y)) 3+ (2z + 7y +7e²³) k. (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about feF. dr where C is the circle (2-15)² + (-10)² = 1 in the zy-plane, oriented clockwise? ScF-dr (c) If C' is any closed curve, what can you say about fodr? JcF-dr=[ (d) Now let C be the half circle (z-15)² + (y-10)² = 1 in the zy-plane with y> 10, traversed from (16, 10) to (14, 10). Find foF-dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. So F df =

Let F = (2x + 2x²) 7+ (7y+7z+ 7 sin(y)) 3+ (2z + 7y +7e²³) k. (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about feF. dr where C is the circle (2-15)² + (-10)² = 1 in the zy-plane, oriented clockwise? ScF-dr (c) If C' is any closed curve, what can you say about fodr? JcF-dr=[ (d) Now let C be the half circle (z-15)² + (y-10)² = 1 in the zy-plane with y> 10, traversed from (16, 10) to (14, 10). Find foF-dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. So F df =

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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Subject: calculus 

 

Let F = (2x +22²) + (7y+7z+7 sin(y)) 3+ (2z+ 7y + 7e²) k (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about feF. dr where C is the circle (z-15)² + (y-10)² = 1 in the zy-plane, oriented clockwise? ScF+dr= (c) If C' is any closed curve, what can you say about fodr? Jc F-dr= (d) Now let C be the half circle (-15)² + (y-10)² = 1 in the zy-plane with y> 10, traversed from (16, 10) to (14, 10). Find fF.dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. SoF dF
Transcribed Image Text:Let F = (2x +22²) + (7y+7z+7 sin(y)) 3+ (2z+ 7y + 7e²) k (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about feF. dr where C is the circle (z-15)² + (y-10)² = 1 in the zy-plane, oriented clockwise? ScF+dr= (c) If C' is any closed curve, what can you say about fodr? Jc F-dr= (d) Now let C be the half circle (-15)² + (y-10)² = 1 in the zy-plane with y> 10, traversed from (16, 10) to (14, 10). Find fF.dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. SoF dF
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