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Problem 6 - Entrance Test

Find the area enclosed by the polar curve r = 2 + cos(θ).

Correct: A

Area = (1/2) ∫[0,2π] r^2 dθ = (1/2) ∫[0,2π] (2 + cos(θ))^2 dθ = (1/2) ∫[0,2π] (4 + 4cos(θ) + cos^2(θ)) dθ = (1/2) ∫[0,2π] (4 + 4cos(θ) + (1 + cos(2θ))/2) dθ = (1/2) [4θ + 4sin(θ) + (1/2)θ + (1/4)sin(2θ)] from 0 to 2π = (1/2) [8π + π] = 9π/2.