平面图形的面积=2∫(2x-x³)dx
=2(x²-x^4/4)│
=2(2-1)
=2；
旋转体体积=2∫π[(2x)²-(x³)²]dx
=2π∫(4x²-x^6)dx
=2π(4x³/3-x^7/7)│
=2π(8√2/3-8√2/7)
=64√2π/21.