24/04/25 15:15:18.22 6S2C/7uf.net
>>529
x = (cosθ)^2 とおくと
√{(1-√x)/(1+√x)} = √{(1-cosθ)/(1+cosθ)}
= (1-cosθ)/sinθ,
dx = -２sinθcosθ dθ,
∫ (1-cosθ)・2cosθ dθ
= ∫ {-1+2cosθ-cos(2θ)} dθ
= －θ + sinθ(2－cosθ),
∴ (与式) = [－θ + sinθ(2－cosθ) ](θ：0→π/2)
= 2－π/2
= 0.4292036732