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Evaluate the integral (xy + xy²) dx + (2x² + x²y) dy over the curve C, defined by going in a straight line from (V2, v2) to (1//2, 1//2), from here to (1//2, –1//2) along the circle x2 +y² = 1, then in a straight line to (/2, – V2), then along the circle x² + y² = 4 back to (v2, v2). See the picture.

Evaluate the integral (xy + xy²) dx + (2x² + x²y) dy over the curve C, defined by going in a straight line from (V2, v2) to (1//2, 1//2), from here to (1//2, –1//2) along the circle x2 +y² = 1, then in a straight line to (/2, – V2), then along the circle x² + y² = 4 back to (v2, v2). See the picture.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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2 to Evaluate the integral | (ry + xy?) dx + (2a² + x²y) dy over the curve C, defined by going in a straight line from (V2, v2) to (1/v2, 1//2), from here to (1//2, –1/V2) along the circle x2 + y² = 1, then in a straight line to (v2, –V2), then along the circle x² + y² = 4 back to (V2, v2). See the picture.
Transcribed Image Text:2 to Evaluate the integral | (ry + xy?) dx + (2a² + x²y) dy over the curve C, defined by going in a straight line from (V2, v2) to (1/v2, 1//2), from here to (1//2, –1/V2) along the circle x2 + y² = 1, then in a straight line to (v2, –V2), then along the circle x² + y² = 4 back to (V2, v2). See the picture.
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