Find the area of the inner loop of the graph

Question

Find the area of the inner loop of the graph. Round answer to two decimal places.

The area of the inner loop is 

Answer 1

Area of inner loop A = 2·1/2∫₀^π(3 - 4cosθ)²dθ = ∫₀^π(9 - 24cosθ + 16cos²θ)dθ = (9θ - 24sinθ + 8θ + 4sin2θ)₀^π = 17π