x=1-2y^2与直线y=x联立得
y=1-2y^2
2y^2+y-1=0
(2y-1)(y+1)=0
y=1/2,y=-1
x=1/2,x=-1
化为定积分得
∫[-1,1/2] (1-2y^2-y)dy
=(y-2y^3/3-y^2/2)[-1,1/2]
=1/2-1/12-1/8+1-2/3+1/2
=9/8求y=x^3,x=1及x轴所围图形绕y轴而形成的旋转体积y=x^3,x=1交点是(0,0)(1,1)体积=π*1^2*1-∫[0,1] π(x^3)^2dx=π-π(x^6)[0,1] =5π/6