∫[0〜2π]√(2+2sinθ) dθ = √2∫[0〜2π]√(1+sinθ) dθ
= √2∫[0〜2π]√{sin^2(θ/2)+cos^2(θ/2)+2sin(θ/2)cos(θ/2)} dθ
= √2∫[0〜2π] |sin(θ/2)+cos(θ/2)| dθ = 2∫[0〜2π] |sin((θ/2)+(π/4))| dθ
= 2*{∫[0〜3π/2] sin((θ/2)+(π/4)) dθ - ∫[3π/2〜2π] sin((θ/2)+(π/4)) dθ}
=4*(2+√2)