求锥面z=√x2+y2，与抛物面z=x2+y2所围立体的体积．
z=√x2+y2与z=x2+y2所围立体在Oxy平面上的投影为 D={(x,y)∣x2+y2≤1}={(r，θ)∣0≤θ≤2π，0≤r≤1}， 所以立体体积V为 V=∫∫D[√(x2+y2)-(x2+y2)]dσ =∫02πdθ∫01(r-r2)rdr=2π[(1/3)r 3 ∣01-(1/4)r4∣01] =π/6
求锥面z=√x2+y2，与抛物面z=x2+y2所围立体的体积．
z=√x2+y2与z=x2+y2所围立体在Oxy平面上的投影为 D={(x,y)∣x2+y2≤1}={(r，θ)∣0≤θ≤2π，0≤r≤1}， 所以立体体积V为 V=∫∫D[√(x2+y2)-(x2+y2)]dσ =∫02πdθ∫01(r-r2)rdr=2π[(1/3)r 3 ∣01-(1/4)r4∣01] =π/6
