Question 16 15. Let P denote the path that goes counter-clockwise around the ellipse² + 4y² = = 1. Find f, F.dr, where F(x, y) = (ª„”).sin (30)16. Let P denote the path parametrized by r(t) = 5 costsin(81)Compute ſpF-dr, where F(x, y, z) = ( „77, ).17. Let F(x, y) = ( ;). Is there a scalar-valued function g(x, y)71 y cos rsin zsin ysuch that F=f? If not explain why, and if so find f.18. Let P be the curve that follows the helix r- sin) from (1,0,0) to(1,3,3), and then returns in a straight line back to (1,0,0). Find31²ynhp0≤t≤ 2π.fg14417

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Answered: Let P denote the path parametrized by…

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 P denote the path parametrized by r(t) = yz Compute fF.dr, where F(x, y, z) = ( IZ #₁). sin(34) 5 cost sin(80) 3), 0≤t 0 < t < 2T.