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filter54321
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Homework Statement
Use double integrals to find the area inside the circle r = 2 cos(θ) and outside the circle r = 1.
Homework Equations
I figured this was too easy to require an graphic. If you can't picture the circles, imagine them in rectangular from:
r = 2 cos(θ) ==> y2+(x-2)2=1
r = 1 ==> y2+x2=1
The Attempt at a Solution
Both circles have a radius of 1 and you need to look at all 2\pi of the objects to see the full area of overlap. So this is what I tried:
[tex]\int\stackrel{2\pi}{0}\int\stackrel{0}{1}[/tex] (2cos(θ)-r) drdθ
The book says the answer is but I can't get it:
[tex]\frac{\pi}{3}[/tex]+[tex]\frac{\sqrt{3}}{2}[/tex]