添加∑1：z=0下侧,由高斯公式：
∫∫∑+∑1=∫∫∫zdxdydz
∫∫∑=-∫∫(∑1)2dxdy+∫∫∫zdxdydz
=8π+(1/2)∫∫(4-x^2-y^2)dxdy
=8π+(1/2)∫(0,2π)dθ∫(0,2)r(4-r^2)dr
=8π+π∫(0,2)(4r-r^3)dr
=12π