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curves3+ co-sis(28) and 1 ss. What is the area founded between the two polar curves?

curves3+ co-sis(28) and 1 ss. What is the area founded between the two polar curves?

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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12.566 17.279 26.704 53.407
Transcribed Image Text:12.566 17.279 26.704 53.407
y The graph above shows the polar -X curves -3+co-sin(28) and 1+sis. What is the area bounded between the two polar curves?
Transcribed Image Text:y The graph above shows the polar -X curves -3+co-sin(28) and 1+sis. What is the area bounded between the two polar curves?
Expert Solution
Step 1

                 The polar equations of the given two regions are  

                            r = 3 + cos θ - sin2θ   and   r = 1 + sinθ   

                The area between the given two regions is 

                               A = ∫θ∫r r dr dθ  -----------(1)

   where  r = inner region r = 1 + sinθ to  upper region  r = 3 + cos θ - sin2θ

                         θ = 0 to 2π  

 

Hence from (1) we get  A = ∫θ=02π∫r = 1 + sinθr = 3 + cos θ - sin2θr dr dθ

 

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