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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.

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.

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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Question 16
15. Let P denote the path that goes counter-clockwise around the ellipse ² + 4y² = = 1. Find f, F.dr, where F(x, y) = (ª„”). sin (30) 16. Let P denote the path parametrized by r(t) = 5 cost sin(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 r sin zsin y such 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). Find 31²y n hp 0≤t≤ 2π. fg 144 17
Transcribed Image Text:15. Let P denote the path that goes counter-clockwise around the ellipse ² + 4y² = = 1. Find f, F.dr, where F(x, y) = (ª„”). sin (30) 16. Let P denote the path parametrized by r(t) = 5 cost sin(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 r sin zsin y such 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). Find 31²y n hp 0≤t≤ 2π. fg 144 17
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