如图所示：
令x=1+cosθ,y=sinθ则原积分=∫(-π/2,π/2) √(2+2cosθ)√((cosθ)^2+(-sinθ)^2)dθ=∫(-π/2,π/2) 2cos(θ/2)dθ=4sin(θ/2) |(-π/2,π/2)=4√2
