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Let C be the arc of the Archemedian spiral r = 0 (where r and are the usual polar coordinates) with 0 ≤ 0 ≤ π/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) (b) Compute the line integrala arctan (2) ds. (c) Consider the vector field F(x, y) = (x²² - y³, 2³). Is F conservative? (d) Compute the flow/F.dr (with F the vector field from part (e)) indirectly by considering

Let C be the arc of the Archemedian spiral r = 0 (where r and are the usual polar coordinates) with 0 ≤ 0 ≤ π/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) (b) Compute the line integrala arctan (2) ds. (c) Consider the vector field F(x, y) = (x²² - y³, 2³). Is F conservative? (d) Compute the flow/F.dr (with F the vector field from part (e)) indirectly by considering

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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Let C' be the arc of the Archemedian spiral r = 0 (where r and are the usual polar coordinates) with 0 ≤ 0 ≤ π/2. (a) Give a parametrization of C. (Hint: Start with the generic r(t) = (x, y), write x and y in polar coordinates, then use the fact that r = = 0 along C) (b) Compute the line integrala arctan (²) ds. (c) Consider the vector field F(x, y) = (x²e² - y³, 2³). Is F conservative? (d) Compute the flow Ja F.dr (with F the vector field from part (c)) indirectly by considering
Transcribed Image Text:Let C' be the arc of the Archemedian spiral r = 0 (where r and are the usual polar coordinates) with 0 ≤ 0 ≤ π/2. (a) Give a parametrization of C. (Hint: Start with the generic r(t) = (x, y), write x and y in polar coordinates, then use the fact that r = = 0 along C) (b) Compute the line integrala arctan (²) ds. (c) Consider the vector field F(x, y) = (x²e² - y³, 2³). Is F conservative? (d) Compute the flow Ja F.dr (with F the vector field from part (c)) indirectly by considering
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