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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 2. (a) (b) 1 F(x,y) = (2√²+2) -1 + tan Y, X 1+ y² Based on (a), what is the value of 3y²). + Show that F is conservative by finding all its potential functions. [F. dŘ? с Use Green's Theorem to set up an iterated double integral equal to f (−y³ + x) dx + (x³ + x²) dy.

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 2. (a) (b) 1 F(x,y) = (2√²+2) -1 + tan Y, X 1+ y² Based on (a), what is the value of 3y²). + Show that F is conservative by finding all its potential functions. [F. dŘ? с Use Green's Theorem to set up an iterated double integral equal to f (−y³ + x) dx + (x³ + x²) dy.

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 2. (a) (b) 1 F(x,y) = (2√²+2) X 3y²). 1+ y² Show that F is conservative by finding all its potential functions. Based on (a), what is the value of [F. dŘ? с Use Green's Theorem to set up an iterated double integral equal to f (−y³ + x) dx + (x³ + x²) dy. -1 + tan Y,
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 2. (a) (b) 1 F(x,y) = (2√²+2) X 3y²). 1+ y² Show that F is conservative by finding all its potential functions. Based on (a), what is the value of [F. dŘ? с Use Green's Theorem to set up an iterated double integral equal to f (−y³ + x) dx + (x³ + x²) dy. -1 + tan Y,
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