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Consider F= (-y, x). (a) Show that F is conservative by finding a potential o. (b) Let C₁ be the circle of radius 1 centered at the origin parametrized by r(t) = (cost, sint). Evaluate F.rds. los (c) Let C₂ be the unit-speed parameterized curve between (0, 1) and (1,0). Calculate fo₂F.rds.

Consider F= (-y, x). (a) Show that F is conservative by finding a potential o. (b) Let C₁ be the circle of radius 1 centered at the origin parametrized by r(t) = (cost, sint). Evaluate F.rds. los (c) Let C₂ be the unit-speed parameterized curve between (0, 1) and (1,0). Calculate fo₂F.rds.

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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Consider F= (-y, x). (a) Show that F is conservative by finding a potential o. (b) Let C₁ be the circle of radius 1 centered at the origin parametrized by r(t) = (cost, sin t). Evaluate So, F.rds. (c) Let C₂ be the unit-speed parameterized curve between (0,1) and (1,0). Calculate fc, F. rds.
Transcribed Image Text:Consider F= (-y, x). (a) Show that F is conservative by finding a potential o. (b) Let C₁ be the circle of radius 1 centered at the origin parametrized by r(t) = (cost, sin t). Evaluate So, F.rds. (c) Let C₂ be the unit-speed parameterized curve between (0,1) and (1,0). Calculate fc, F. rds.
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