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Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment from (0, 0) to (−1, 1), and C3 is the portion of the circle x² + y² = 2 from (−1, 1) to (-1,-1) traced counterclockwise. 1 2 √√x+2 Define F(x, y) = x + tan-¹y, 1+y² a. Show that is conservative by finding all its potential functions. b. Based on (a), what is the value of ♫ ♬ · dŘ? + 3y²>.

Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment from (0, 0) to (−1, 1), and C3 is the portion of the circle x² + y² = 2 from (−1, 1) to (-1,-1) traced counterclockwise. 1 2 √√x+2 Define F(x, y) = x + tan-¹y, 1+y² a. Show that is conservative by finding all its potential functions. b. Based on (a), what is the value of ♫ ♬ · dŘ? + 3y²>.

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 = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C2 is the line segment from (0, 0) to (−1, 1), and C3 is the portion of the circle x² + y² = 2 from (−1, 1) to (-1,-1) traced counterclockwise. 1 Define F(x, y) =< + tan´¹y, +3y² >. 2 √x+2 x 1+y² a. Show that is conservative by finding all its potential functions. b. Based on (a), what is the value of SF · dR?
Transcribed Image Text:Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C2 is the line segment from (0, 0) to (−1, 1), and C3 is the portion of the circle x² + y² = 2 from (−1, 1) to (-1,-1) traced counterclockwise. 1 Define F(x, y) =< + tan´¹y, +3y² >. 2 √x+2 x 1+y² a. Show that is conservative by finding all its potential functions. b. Based on (a), what is the value of SF · dR?
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