How do you find the area of the region shared by the circles r=2cos(θ) and r=2sin(θ)?

1 Answer
Oct 24, 2015

π21

Explanation:

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Intersection:
2sinθ=2cosθsinθcosθ=1tanθ=1θ=π4

A=Ardrdθ

A=π40dθ2sinθ0rdr+π2π4dθ2cosθ0rdr

A1=12π40dθ4sin2θ=π40(1cos2θ)dθ

A1=(θ12sin2θ)π40=π412

A2=12π2π4dθ4cos2θ=π2π4(1+cos2θ)dθ

A2=(θ+12sin2θ)π2π4=π412

A=π412+π412=π21