y=sinx(0<=x<=π)与x轴围成图形绕y轴旋转所得旋转体的体积S=∫<0,1>π[(π-arcsiny)^2-(arcsiny)^2]dy设u=arcsiny属于[0,π/2],则y=sinu,dy=cosudu,S=π∫<0,π/2>[(π-u)^2-u^2]cosudu=π∫<0,π/2>(π^2-2πu)cosudu=π^2[πsinu-2usinu-2cosu]|<0,π/2>=2π^2.
