1.曲线Y=3X^3Y=0 X=0 X=2 所围成的图形的面积
S=∫(0,2)3X^3dx=(3/4)*16=12
绕X轴的体积V=π∫(0,2)(3X^3)^2dx=9π∫(0,2)X^6dx=(9π/7)*128=1152π/7
绕y轴的体积V=2π∫(0,2)x3X^3dx=6π∫(0,2)X^4dx=(6π/5)*32=192π/5
2曲线Y=X^2及直线Y=2X所围成图形的面积.交点(0,0), (2,4)
S=∫(0,2)(2x-x^2)dx=(x^2-x^3/3)|(0,2)=4-8/3=4/3
绕X轴的体积V=π∫(0,2)(2x)^2dx-π∫(0,2)(x^2)^2dx
=π(32/3-32/5)=64π/15
绕y轴的体积V=2π∫(0,2)x(2x)dx-2π∫(0,2)x(x^2)dx
=2π(16/3-4)=8π/3