原第一类曲面积分
= ∯<∑> x^2dydz + y^2dxdz + z^2dxdy (用
高斯公式)
= ∫∫∫<Ω>(2x+2y+2z)dxdydz
= 2∫<0, h>dz∫<0, 2π>dt∫<0, z>(rcost+rsint+z)rdr
= 2∫<0, h>z^3dz∫<0, 2π>[(1/3)(cost+sint)+(1/2)]dt
= 2∫<0, h>z^3dz[(1/3)(sint-cost)+(1/2)t]<0, 2π>
= 2π[z^4/4]<0, h> = (π/2)h^4