计算由旋转抛物面z=1+x2+y2与柱面x2+y2=1所围成的立体的体积V．
V=∫∫D(1+x2+y2)dxdy (D：x2+y2 ≤1) =∫∫D(1+r2)•rdrdθ=∫02πdθ∫01(1+r2)rdr =2π(r2/2+r4/4)∣01=(3/2)π
计算由旋转抛物面z=1+x2+y2与柱面x2+y2=1所围成的立体的体积V．
V=∫∫D(1+x2+y2)dxdy (D：x2+y2 ≤1) =∫∫D(1+r2)•rdrdθ=∫02πdθ∫01(1+r2)rdr =2π(r2/2+r4/4)∣01=(3/2)π
