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Let C denote the curve that starts at the point (1,0), traverses the unit circle to the point (0, –1) then follows a straight line to (1,–1). Let F be the vector field F(x, y) = (-a, a), where a is a constant. Find the value(s) of a, if any, such that F. dī is equal to the arc-length of C.

Let C denote the curve that starts at the point (1,0), traverses the unit circle to the point (0, –1) then follows a straight line to (1,–1). Let F be the vector field F(x, y) = (-a, a), where a is a constant. Find the value(s) of a, if any, such that F. dī is equal to the arc-length of C.

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 C denote the curve that starts at the point (1,0), traverses the unit circle to the point (0, –1) then follows a straight line to (1,–1). Let F be the vector field F(x, y) = (-a, a), where a is a constant. Find the value(s) of a, if any, such that F. dī is equal to the arc-length of C.
Transcribed Image Text:Let C denote the curve that starts at the point (1,0), traverses the unit circle to the point (0, –1) then follows a straight line to (1,–1). Let F be the vector field F(x, y) = (-a, a), where a is a constant. Find the value(s) of a, if any, such that F. dī is equal to the arc-length of C.
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