a) The region R lies inside the curve r = v2 sin 0 (for 0 <0 <7) and outside the unit circle r = 1. Sketch this region R and evaluate its area. %3D
a) The region R lies inside the curve r = v2 sin 0 (for 0 <0 <7) and outside the unit circle r = 1. Sketch this region R and evaluate its area. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Needed to be solved part a complete in 20 minutes and get the 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc2d5068-03e4-4cff-b5a4-f8e0cb916b03%2Fbf79737d-257e-408a-aa6d-6ebdb4057306%2Fghv3ys_processed.jpeg&w=3840&q=75)
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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