看下图
1.用柱坐标做：x=rcosθ,y=rsinθ,z=z,dv=rdrdθdz, ∫∫∫z^2dV= ∫[-π/2,π/2]dθ∫[0,Rcosθ]rdr∫[-√(R^2-r^2),√(R^2-r^2)]z^2dz =∫[-π/2,π/2]dθ∫[0,Rcosθ]rdr(2/3)*(R^2-r^2)^(3/2) =∫[-π/2,π/2]dθ(2/15)*R^5*(1-(sinθ)^5) =2πR^5/15. 我就会第一道
