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Let P = (42+42²) + (7y + 5z +5 sin(y)) 3+ (4z + 5y + 7e) k (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about foF-dr where C is the circle (z-35)2+(-35)2-1 in the zy-plane, oriented clockwise? JcF-dF= (c) If C is any closed curve, what can you say about fcF-di? SoF-dr= (d) Now let C be the half circle (z-35)² + (y-35)² = 1 in the zy-plane with y> 35, traversed from (36, 35) to (34, 35). Find fF-dF by using your result from (c) and considering C plus the line segment connecting the endpoints of C. SoF-dr=

Let P = (42+42²) + (7y + 5z +5 sin(y)) 3+ (4z + 5y + 7e) k (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about foF-dr where C is the circle (z-35)2+(-35)2-1 in the zy-plane, oriented clockwise? JcF-dF= (c) If C is any closed curve, what can you say about fcF-di? SoF-dr= (d) Now let C be the half circle (z-35)² + (y-35)² = 1 in the zy-plane with y> 35, traversed from (36, 35) to (34, 35). Find fF-dF by using your result from (c) and considering C plus the line segment connecting the endpoints of C. SoF-dr=

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 = (42+42²) + (7y+52 +5 sin (32)) 3+ (42+ 5y + 7e²¹) k (a) Find curl F. curl F= (b) What does your answer to part (a) tell you about fodr where C is the circle (-35)2+(y-35)2-1 in the zy-plane, oriented clockwise? SoF dF= (c) If C is any closed curve, what can you say about fF.dr? SoF-dF= (d) Now let C be the half circle (z-35)2+(-35)² = 1 in the zy-plane with y> 35, traversed from (36, 35) to (34, 35). Find JF dF by using your result from (c) and considering C plus the line segment connecting the endpoints of C. SoF-dr=
Transcribed Image Text:Let = (42+42²) + (7y+52 +5 sin (32)) 3+ (42+ 5y + 7e²¹) k (a) Find curl F. curl F= (b) What does your answer to part (a) tell you about fodr where C is the circle (-35)2+(y-35)2-1 in the zy-plane, oriented clockwise? SoF dF= (c) If C is any closed curve, what can you say about fF.dr? SoF-dF= (d) Now let C be the half circle (z-35)2+(-35)² = 1 in the zy-plane with y> 35, traversed from (36, 35) to (34, 35). Find JF dF by using your result from (c) and considering C plus the line segment connecting the endpoints of C. SoF-dr=
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