22 + y?. x2 + y? Consider the vector field F |3D x2 + y2" (a) Show that F dr = 27 for all e >0 (b) Show that F is conservative away from the origin and find it's potential (c) Prove that F. dr = 27 for any closed curve C enclosing the origin

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a2 + y² – Y;+
x² + y?
|
Consider the vector field F=
x2 + y2°
(a) Show that
F dr = 27 for all e > 0
2²+y²=e
(b) Show that F is conservative away from the origin and find it's potential
(c) Prove that
F. dr = 27 for any closed curve C enclosing the origin
Transcribed Image Text:a2 + y² – Y;+ x² + y? | Consider the vector field F= x2 + y2° (a) Show that F dr = 27 for all e > 0 2²+y²=e (b) Show that F is conservative away from the origin and find it's potential (c) Prove that F. dr = 27 for any closed curve C enclosing the origin
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