这是第一类曲面积分。z = ±√(a^2-x^2-y^2),I = ∯<∑>z^2dS = 2 ∫∫ z^2√[1+(z)^2+(z)^2] dxdy = 2 ∫∫ (a^2-x^2-y^2)a/√(a^2-x^2-y^2) dxdy = 2a ∫∫ √(a^2-x^2-y^2) dxdy = 2a ∫<0,2π>dt ∫<0,a> √(a^2-r^2) rdr = -2πa ∫<0,a> √(a^2-r^2) rd(a^2-r^2) = -2πa [(2/3)(a^2-r^2)^(3/2)]<0,a> = (4/3)πa^4
