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Let F(r, y) = (2re-")i+ (2y – x²e=v)j. (a) Show there exists a function f(r, y) such that Vf = F. (b) Find f(x, y) such that Vf = F. (c) Calculate 2.re "dx + (2y – ²e")dy where C is the unit octagon centered at the origin, oriented clockwise.

Let F(r, y) = (2re-")i+ (2y – x²e=v)j. (a) Show there exists a function f(r, y) such that Vf = F. (b) Find f(x, y) such that Vf = F. (c) Calculate 2.re "dx + (2y – ²e")dy where C is the unit octagon centered at the origin, oriented clockwise.

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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2. Let F(r, y) = (2re ")i+ (2y – 2²e")j. (a) Show there exists a function f(r, y) such that Vf = F. (b) Find f(x, y) such that Vf = F. (c) Calculate 2xedr + (2y – re-")dy where C is the unit octagon centered at the origin, oriented clockwise.
Transcribed Image Text:2. Let F(r, y) = (2re ")i+ (2y – 2²e")j. (a) Show there exists a function f(r, y) such that Vf = F. (b) Find f(x, y) such that Vf = F. (c) Calculate 2xedr + (2y – re-")dy where C is the unit octagon centered at the origin, oriented clockwise.
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