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Homework Help
Calculus and Beyond Homework Help
Finding the area between Polar Curves
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[QUOTE="jojo13, post: 4743576, member: 497022"] [h2]Homework Statement [/h2] Find the area of the region that consists of all points that lie [B]within[/B] the circle r = 1 but [B]outside[/B] the polar equation r = cos(2θ) [h2]Homework Equations[/h2] A = ∫ 1/2 (r2^2 - r1^2) dθ, where r2 is outer curve and r1 is inner curve. [h2]The Attempt at a Solution[/h2] Here is what the graph looks like if you want to see it: [url]http://www.wolframalpha.com/input/?i=r+%3D+cos%282x%29+polar[/url] Ok so first I had to find out the limits for my integral. I set: 1 = cos(2θ) and got that θ = ∏. Now I made my integral, but instead of going from -∏ to ∏ I went from 0 to ∏ and multiplied it by 2 A = 2 ∫ 1/2 [(1^2) - (cos(2θ)^2)] dθ, from 0 to ∏ A = ∫ [ (1) - (1/2 cos(4θ) +1)] dθ, from 0 to ∏ I solved it and received: ∏ - ∏/2 Which equals ∏/2. Just want to know if I did it right. The main part I was worried about was the limits for my integral. [/QUOTE]
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Finding the area between Polar Curves
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