旋转抛物面,对称,xoy平面为半径2圆,只取一卦限体积,再乘4,转换为极坐标,D:0≤θ≤π/2,0≤r≤2,V=4 ∫[0,π/2]dθ∫[0,2](4-r^2)rdr
=4 ∫[0,π/2]dθ(2r^2-r^4/4)[0,2)
=4 ∫[0,π/2]4dθ
=8π.
旋转抛物面,对称,xoy平面为半径2圆,只取一卦限体积,再乘4,转换为极坐标,D:0≤θ≤π/2,0≤r≤2,V=4 ∫[0,π/2]dθ∫[0,2](4-r^2)rdr
=4 ∫[0,π/2]dθ(2r^2-r^4/4)[0,2)
=4 ∫[0,π/2]4dθ
=8π.