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X. Let C = C₁ UC₂U 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 (a) (b) 1 2√x + 2 X F(x, y) = 1 + y² Show that F is conservative by finding all its potential functions. Based on (a), what is the value of Joi F. dR? + tan Y, (33²). +3y

X. Let C = C₁ UC₂U 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 (a) (b) 1 2√x + 2 X F(x, y) = 1 + y² Show that F is conservative by finding all its potential functions. Based on (a), what is the value of Joi F. dR? + tan Y, (33²). +3y

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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X. 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 (a) (b) 1 F(x, y) = (2 + tan²¹ y. ₁+²+3y²) Y, 2√x + 2 1+ Show that F is conservative by finding all its potential functions. F.dR? [F Based on (a), what is the value of
Transcribed Image Text:X. 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 (a) (b) 1 F(x, y) = (2 + tan²¹ y. ₁+²+3y²) Y, 2√x + 2 1+ Show that F is conservative by finding all its potential functions. F.dR? [F Based on (a), what is the value of
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