Find the area of the region that lies inside the first curve and outside the second curve.

Question

r = 14 cos 𝜃, r = 7

Answer 1

the curves intersect at θ = ±π/3 so using the symmetry of the region, its area
a = 2∫[0,π/3] 1/2 (R^2 - r^2) dθ
where R = 14cosθ and r=7
a = ∫[0,π/3] ((14cosθ)^2 - 7^2) dθ = 49/6 (3√3 + 2π)