令P=yz,Q=0,R=x+2y+z,则αP/αx=0,αQ/αy=0,αR/αz=1
故 由奥高公式得
∫∫(x+2y+z)dxdy+yzdydz=∫∫yzdydz+0*dzdx+(x+2y+z)dxdy
=∫∫Pdydz+Qdzdx+Rdxdy
=∫∫∫(αP/αx+αQ/αy+αR/αz)dxdydz (V是Σ所围成的空间体积)
=∫∫∫(0+0+1)dxdydz
=∫dx∫dy∫dz
=∫dx∫(6-x-2y)dy
=∫(9-3x+x²/4)dx
=18.