Let C be the arc of the Archemedian spiral r = 0 (where r and are the usual polar coordinates) with 0 ≤ 0 ≤T/2. (a) Give a parametrization of C. (Hint: Start with the generic r(t) = (x, y), writer and y in polar coordinates, then use the fact that r = 0 along C) ¹ (²) ds. (c) Consider the vector field F(x, y) = (x²e² - y³, 2³). Is F conservative? (b) Compute the line integral ar arctan
Let C be the arc of the Archemedian spiral r = 0 (where r and are the usual polar coordinates) with 0 ≤ 0 ≤T/2. (a) Give a parametrization of C. (Hint: Start with the generic r(t) = (x, y), writer and y in polar coordinates, then use the fact that r = 0 along C) ¹ (²) ds. (c) Consider the vector field F(x, y) = (x²e² - y³, 2³). Is F conservative? (b) Compute the line integral ar arctan
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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