所围图形的面积=∫(e-e^y)dy
=(ey-e^y)│
=e-e+1
=1；
旋转体体积=π∫ln²xdx
=π(e-2∫lnxdx) (应用分部积分法)
=π(e-2e+2∫dx) (应用分部积分法)
=π(e-2e+2(e-1))
=π(e-2).