LikeIke550 LikeIke550
  • 14-05-2018
  • Mathematics
contestada

Find the area of the region inside the circle (x-1)^2+y^2=1 and outside the circle x^2+y^2=1

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sqdancefan
sqdancefan sqdancefan
  • 16-05-2018
There are numerous ways to approach this. Perhaps the simplest is to subtract twice the area of the shaded segment (see the attached figure) from that of the circle.

The area of the shaded segment is
  segment area = (1/2)r^2*(θ -sin(θ))
where r=1 and θ=2π/3

The area of the circle, of course, is πr^2 = π, so the area of interest is ...
  A = π -(2π/3 -sin(2π/3))
  A = π/3 +(√3)/2
Ver imagen sqdancefan
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