∵x=rsinφcosθ,y=rsinφsinθ,z=rcosφ
│αx/αr αx/αφ αx/αθ│ │sinφcosθ rcosφcosθ -rsinφsinθ │
∴α(x,y,z)/α(r,φ,θ)=│αy/αr αy/αφ αy/αθ│=│sinφsinθ rcosφsinθ rsinφcosθ│=r²sinφ
│αz/αr αz/αφ αz/αθ│ │cosφ -rsinθ 0 │
∵dxdydz=│α(x,y,z)/α(r,φ,θ)│drdφdθ=r²sinφdrdφdθ
∴∫∫∫f(x,y,z)dxdydz=∫∫∫F(r,φ,θ)r²sinφdrdφdθ.