(a) Plot the spiral r() = for 0 8. (b) On your plot, shade in the region that represents the increase

(a) Plot the spiral r(θ) = θ for 0 ≤ θ ≤ 8π.
(b) On your plot, shade in the region that represents the increase in area enclosed by the curve as θ goes from 6π to 8π. Compute the shaded area.
(c) Show that the increase in area enclosed by the graph of r(θ) as θ goes from 2nπ to 2(n + 1)π is 8n.