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a) The region R lies inside the curve r v2 sin 0 (for 0<0

a) The region R lies inside the curve r v2 sin 0 (for 0<0

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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Only part a needed in 10 minutes and get thumbs up please show neat and clean work
a) The region R lies inside the curve r = v2 sin 0 (for 0 <0 < n) and outside the unit circle r = 1. Sketch this region R and evaluate its area. b) F = (2r – 32*)i + zj + (y – 6rz)k. UN i) Evaluate div F. ii) Evaluate curl F. iii) Evaluate the vector line integral of F, F. ds, where y is an oriented curve defined as follows: (t) = sin? ti + cos 2f j+ e' k, 0<t<n. c) Let C be the circle r? + y? = 4 oriented in a counterclockwise direction. Use %3D Green's theorem to evaluate | (2y - ) dr + (3r + Vy' + 2) dy.
Transcribed Image Text:a) The region R lies inside the curve r = v2 sin 0 (for 0 <0 < n) and outside the unit circle r = 1. Sketch this region R and evaluate its area. b) F = (2r – 32*)i + zj + (y – 6rz)k. UN i) Evaluate div F. ii) Evaluate curl F. iii) Evaluate the vector line integral of F, F. ds, where y is an oriented curve defined as follows: (t) = sin? ti + cos 2f j+ e' k, 0<t<n. c) Let C be the circle r? + y? = 4 oriented in a counterclockwise direction. Use %3D Green's theorem to evaluate | (2y - ) dr + (3r + Vy' + 2) dy.
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