y=x^2绕y轴一周的立体体积减去y=x^2+1绕y轴一周的立体体积分即可
将两曲线写为：x=√y,x=√(y-1)
dV1=π(√y)^2dy
则V1=π∫[0-->2](√y)^2dy
=π∫[0-->2]ydy
=π/2y^2 [0-->2]
=2π
dV2=π(√(y-1))^2dy
V2=π∫[1-->2](√(y-1))^2dy
=π∫[1-->2](y-1)dy
=π/2*y^2-πy [1-->2]
=π/2
因此所求体积为：V1-V2=2π-π/2=3π/2
y=x^2绕y轴一周的立体体积减去y=x^2+1绕y轴一周的立体体积分即可
将两曲线写为：x=√y,x=√(y-1)
dV1=π(√y)^2dy
则V1=π∫[0-->2](√y)^2dy
=π∫[0-->2]ydy
=π/2y^2 [0-->2]
=2π
dV2=π(√(y-1))^2dy
V2=π∫[1-->2](√(y-1))^2dy
=π∫[1-->2](y-1)dy
=π/2*y^2-πy [1-->2]
=π/2
因此所求体积为：V1-V2=2π-π/2=3π/2