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The regon, D, is the region enclosed by the parametric curve: r(t) = vector brackets (cos(t), sin(t) - cos(t)) O <= t <= 2pi %3D Some people call the region D, "the Dude" or "His Dudness". Find the area of, D, by using Green's Theorem.

The regon, D, is the region enclosed by the parametric curve: r(t) = vector brackets (cos(t), sin(t) - cos(t)) O <= t <= 2pi %3D Some people call the region D, "the Dude" or "His Dudness". Find the area of, D, by using Green's Theorem.

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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The regon, D, is the region enclosed by the parametric curve: r(t) = vector brackets (cos(t), sin(t) - cos(t)) O <=t<= 2pi Some people call the region D, "the Dude" or "His Dudness". Find the area of, D, by using Green's Theorem. А.) 0 В.) pi C.) -pi D.) 2pi E.) none of these
Transcribed Image Text:The regon, D, is the region enclosed by the parametric curve: r(t) = vector brackets (cos(t), sin(t) - cos(t)) O <=t<= 2pi Some people call the region D, "the Dude" or "His Dudness". Find the area of, D, by using Green's Theorem. А.) 0 В.) pi C.) -pi D.) 2pi E.) none of these
Expert Solution
Step 1

Given that the region D is enclosed by the parametric curve, 

rt=cost, sint-cost with 0≤t≤2π

Area of D is given by, 

∬DdA

Then, by Greens theorem, we have, 

∬DdA=∮CF·ds

∬DdA=∫02πgtf'tdt...........................(1)

where, gt=sint-cost and ft=cost.

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