4. Calculate: (1,0,2π) (a) | zd. +xdy+ydz (b) (1,0,0) along the curve with the parametrisation x(t) = (cost, sint, t), 0 ≤ t ≤ 2π; (2,3,2) [ x²dx − xzdy + y²dz (1,0,1) along the straight line that connects the starting and endpoints; (1,0,2) dx + (x² + y² + z²)dz (0,1,0) Y along the curve in the first octant given by x² + y² = 1, z = 2x; (0,0,2) (d) \ (2,0,0) ydxy(x 1)dy + y²zdz - along the curve in the first octant given by x² + y² + z² = 4, (x − 1)² + y² = 1.
4. Calculate: (1,0,2π) (a) | zd. +xdy+ydz (b) (1,0,0) along the curve with the parametrisation x(t) = (cost, sint, t), 0 ≤ t ≤ 2π; (2,3,2) [ x²dx − xzdy + y²dz (1,0,1) along the straight line that connects the starting and endpoints; (1,0,2) dx + (x² + y² + z²)dz (0,1,0) Y along the curve in the first octant given by x² + y² = 1, z = 2x; (0,0,2) (d) \ (2,0,0) ydxy(x 1)dy + y²zdz - along the curve in the first octant given by x² + y² + z² = 4, (x − 1)² + y² = 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
Question
Usually, when these questions are asked, x=cost and y =sint, I'm confused as to why they are switched in the worked solutions here and how they got the value for z initially.
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