1.曲線Y=3X^3Y=0 X=0 X=2 所圍成的圖形的面積
S=∫(0,2)3X^3dx=(3/4)*16=12
繞X軸的體積V=π∫(0,2)(3X^3)^2dx=9π∫(0,2)X^6dx=(9π/7)*128=1152π/7
繞y軸的體積V=2π∫(0,2)x3X^3dx=6π∫(0,2)X^4dx=(6π/5)*32=192π/5
2曲線Y=X^2及直線Y=2X所圍成圖形的面積.交點(diǎn)(0,0), (2,4)
S=∫(0,2)(2x-x^2)dx=(x^2-x^3/3)|(0,2)=4-8/3=4/3
繞X軸的體積V=π∫(0,2)(2x)^2dx-π∫(0,2)(x^2)^2dx
=π(32/3-32/5)=64π/15
繞y軸的體積V=2π∫(0,2)x(2x)dx-2π∫(0,2)x(x^2)dx
=2π(16/3-4)=8π/3