求∫∫∫A(x^2+y^2)dv其中A是由曲线y^2=2z和x=0绕z轴旋转一周而成的曲面与平面z=4

旋转曲面方程为：x²+y²=2z,与平面z=4交线为：x²+y²=8
∫∫∫ (x²+y²) dv
=∫∫∫ r²*r dzdrdθ
=∫[0→2π]dθ∫[0→2√2]r³dr∫[0→r²/2] dz
=2π∫[0→2√2]r^5/2dr
=π∫[0→2√2]r^5dr
=(π/6)r^6 |[0→2√2]
=256π/3