Question

高数，用定积分求绕指定轴旋转所构成的旋转体的体积

Answer 1

dV=[π(x+dx)^2-πx^2]y
=2πxydx=2πadx
dV以x+dx为外径，x为内径，y为高的圆环柱体体积，
V=∫2πadx=[2πax]=2πa^2

Answer 2

∫(a/x) dx [积分上限2a，下限a]
= - a/x^2 [上限2a，下限a]
= 3/(4a)