Question Number 113868 by Ar Brandon last updated on 15/Sep/20

Find the area between the circle ρ=2acosθ and   cardiode ρ=a(1+cosθ)

Commented bykaivan.ahmadi last updated on 18/Sep/20

2acosθ=a+acosθ⇒acosθ=a⇒cosθ=1⇒  θ=0,θ=2π  ∫_0 ^(2π) ((2acosθ)^2 −(a(1+cosθ))^2 )dθ=  ∫_0 ^(2π) (4a^2 cos^2 θ−a^2 cos^2 θ−2a^2 cosθ−a^2 )dθ=  a^2 ∫_0 ^(2π) (3cos^2 θ−2cosθ−1)dθ=  a^2 (((3θ)/2)−((3sin2θ)/4)−2sinθ−θ∣_0 ^(2π) )=  a^2 [(3π−0−0−2π)−(0−0−0−0)]=  a^2 π