Find the area enclosed by the curve

Question

Find the area enclosed by the curve r= 10(1+cos(theta)).

Answer 1

r = 10(1 + cosθ); Area A = 2·1/2∫₀^π100(1 + cosθ)²dθ = 100∫₀^π(1 + 2cosθ + cos²θ)dθ = 100(θ + 2sinθ + 1/2θ +

1/4sin2θ)₀^π = 100(3/2π) = 150π^