曲线 y = x,y = 1/x,x = 2 与 y = 0 所围成的平面图形是:
直线 y = x,曲线 y = 1/x 之下, x 轴之上,直线 x = 2 之左 的区域,
可自行画图。直线 y = x 与曲线 y = 1/x 交于点 (1, 1).
V = π [ ∫<0, 1>x^2dx + ∫<1, 2>(1/x^2)dx ]
= π[x^3/3]<0, 1> + π[-1/x]<1, 2>
= π/3 + π/2 = 5π/6
S=ʃ[0,1]xdx+ʃ[1,2](1/x)dx
=(x²/2)|[0,1]+(lnx)|[1,2]
=1/2+ln2;
Vx=πʃ[0,1]x²dx+πʃ[1,2](1/x)²dx
=π(x³/3)|[0,1]+π(-1/x)|[1,2]
=π/3+π/2
=5π/6 .