Chapter 16.3, Problem 72E

Area formula In Section 12.3 it was shown that the area of a region enclosed by the polar curve r = g(θ) and the rays θ = α and θ = β, where β − α ≤ 2π, is $A=\frac{1}{2}{\displaystyle {\int }_{\alpha }^{\beta }{r}^{2}d\theta }$. Prove this result using the area formula with double integrals.