利用对称性:∫∫∫Ω(x+z)dv = ∫∫∫Ω(z)dv
换成球坐标:z = r cosφ, x = r sinφ cos θ, y = r sinφ sin θ
r from 0 to 1; φ from 0 to pi/4; θ from 0 to 2pi
∫∫∫Ω(z)dv = ∫[0,2pi] d θ ∫[0, pi/4] dφ ∫[0,1] rcosφ r^2sinφ dr
= (pi/4) ∫[0, pi/4] sin φ cos φ dφ
= (pi/4)(1/2)sin^2φ from 0 to pi/4
= pi/16