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Use integration to find the area of the region outside the circle r=1/2 and inside the circle of r=cos(theta)?
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- cidyahLv 79 years agoFavorite Answer
cos(theta)=1/2
theta = pi/3, 5pi/3
theta = -pi/3, pi/3
Area = (1/2) ∫ r^2 dθ
Area = (1/2) ∫ [cos^2(θ) - (1/2)^2 ] dθ , from -pi/3 to pi/3
Area = (1/2) ∫ [cos^2(θ) - 1/4 ] dθ , from -pi/3 to pi/3
Source(s): http://www.wolframalpha.com/input/?i=polar+plot+r%... http://www.wolframalpha.com/input/?i=polar+plot+r%... - 9 years ago
the equasion of a circule is x^2 + y^2 = r^2
so your formula is x^2 + y^2 = (1/2)^2 you should be able to intergrate that if that is your homework. it should be in a table some place....
Source(s): http://en.wikipedia.org/wiki/Lists_of_integrals http://www.regentsprep.org/Regents/math/algtrig/AT...
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