Find the area enclosed by r = θ, and the interval [0, 2π]

Question

on the x-axis.

Answer 1

A = ∫[0,2π] 1/2 r^2 dθ = ∫[0,2π] 1/2 r^2 dθ = ∫[0,2π] 1/2 θ^2 dθ
= 1/6 θ^3 [0,2π] = 4/3 π^3