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. - Compute F dR around the closed path consisting of a circle of radius r, centered at the origin, in the xy plane, taking F = (-yi+xj)/(x² + y²) (Hint: Change to polar coordinates.) If you worked correctly, you obtained a nonzero answer to exercise 4. Yet it appears that F = grad o, where o = tan-¹(v/x), and this would contradio

. - Compute F dR around the closed path consisting of a circle of radius r, centered at the origin, in the xy plane, taking F = (-yi+xj)/(x² + y²) (Hint: Change to polar coordinates.) If you worked correctly, you obtained a nonzero answer to exercise 4. Yet it appears that F = grad o, where o = tan-¹(v/x), and this would contradio

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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• - Compute F dR around the closed path consisting of a circle of radius r, centered at the origin, in the xy plane, taking F = (-yi+xj)/(x² + y²) (Hint: Change to polar coordinates.) F = If you worked correctly, you obtained a nonzero answer to exercise 4. Yet it appears that grad o, where = tan-¹(y/x), and this would contradict theorem 4.2. Investigate this mystery. Find a potential
Transcribed Image Text:• - Compute F dR around the closed path consisting of a circle of radius r, centered at the origin, in the xy plane, taking F = (-yi+xj)/(x² + y²) (Hint: Change to polar coordinates.) F = If you worked correctly, you obtained a nonzero answer to exercise 4. Yet it appears that grad o, where = tan-¹(y/x), and this would contradict theorem 4.2. Investigate this mystery. Find a potential
coincide, the -O around every regu (see exercise 1 for the proof). THEOREM 4.2 A vector field F continuous in a domain D is conservative if and only if around every regular closed curve in D the line integral of F (i.e., its circulation) is zero. ry² + x³yj is not conservative.
Transcribed Image Text:coincide, the -O around every regu (see exercise 1 for the proof). THEOREM 4.2 A vector field F continuous in a domain D is conservative if and only if around every regular closed curve in D the line integral of F (i.e., its circulation) is zero. ry² + x³yj is not conservative.
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