计算I=∬∑xdS其中∑：x2+y2+z2=R2．

计算
I=∬_∑xdS
其中∑：x²+y²+z²=R²．
【正确答案】：I=∬_∑x²dS=2∬_Dxy√1+z_x²+z_t²dxdy =2∬_Dxy(Rx²/√R²-x²-y²)dxdy =2R∫₀^2πdθ∫₀^R(r³cos²θ/√R²-r²)dr =2Rd∫₀^2π[(1++cos2θ)/2]∫₀^R(r³dr/√R²-r²) =2R•π•(2/3)R³=(4/3)πR⁴