>>332
S = 2π∫[0,π] sin(x)･√{1+cos(x)^2} dx
　= 2π∫[-1,1] √(1+z^2) dz
　= 4π∫[0,1] √(1+z^2) dz
　= 2π [ z√(1+z^2) + log| z+√(1+z^2) | ](z:0→1)
　= 2π{ √2 + log(1+√2) }.