根据x,y,z的对等性
所以∫x^2dS=∫y^2dS=∫z^2dS
∫xdS=∫ydS=∫zdS
所以∫xdS=∫ydS=∫zdS=(1/3)∫(x+y+z)dS=0
所以
原积分=∫x^2dS+2∫ydS+∫zdS=∫x^2dS=(1/3)∫(x^2+y^2+z^2)dS=(1/3)∫dS=2π/3
根据x,y,z的对等性
所以∫x^2dS=∫y^2dS=∫z^2dS
∫xdS=∫ydS=∫zdS
所以∫xdS=∫ydS=∫zdS=(1/3)∫(x+y+z)dS=0
所以
原积分=∫x^2dS+2∫ydS+∫zdS=∫x^2dS=(1/3)∫(x^2+y^2+z^2)dS=(1/3)∫dS=2π/3