Find the area of the region that is inside the graph of r = 1 and outside of the graph of r = 1 + cos (θ). (4 points)

Question

A) 1.127
B) 1.215
C) 1.275
D) 1.375

Answer 1

The curves intersect where
1+cosθ = 1
θ = ±π/2
But we want the left side of the graphs, so using symmetry
A = 2∫[π/2, 3π/2] 1/2 (1^2 - (1+cosθ)^2) dθ
= ∫[π/2, 3π/2] -2cosθ - cos^2θ dθ
Now finish it off.