(a) Find a formula for the area of the surface generated by rotating the polar curve r = f(θ), a ≤ θ ≤ b (where f' is continuous and 0 ≤ a < b ≤ π), about the line θ = π/2.

(b) Find the surface area generated by rotating the lemniscate r² = cos 2θ about the line θ = π/2.