求体积,

y=x^2+2, ∴x^2=y-2交点:x=0,y=2, x=1,y=3x=1,y=0,y=2绕y轴旋转一周所得的圆柱体积=2*π总体积V=2*π+∫(2,3)π(1-x²)dy=2*π+∫(2,3)π(3-y)dy∫π(3-y)dy=3πy-πy²/2+C∴总体积V=2*π+∫(2,3)π(3-y)dy=2*π+[3π-(π/2)*(3^2-2^2)]=2*π+π/2=2。5π