z=√(x^2+y^2)是一个上锥面的漏斗形,在XOY平面投影是由x^2+y^2=1所围成,
转换为柱面坐标,0≤r≤1,0≤θ≤2π,r≤z≤1
I=∫∫∫[Ω]zdzdydx
=∫[0,2π]dθ∫[0,1] rdr∫[r,1]zdz
=∫[0,2π]dθ∫[0,1](1/2(1-r^2) rdr
=(1/2)∫[0,2π]dθ∫[0,1](r-r^3)dr
=(1/2)∫[0,2π][0,1](r^2/2-r^4/4)dθ
=(1/2)∫[0,2π](1/4)dθ
=(1/8)*2π
=π/4.