MathDB

Let

(a,\ b)

be a point on the curve

y=\frac{x}{1+x}\ (x\geq 0).

Denote

U

the volume of the figure enclosed by the curve , the

x

axis and the line

x=a

, revolved around the the

x

axis and denote

V

the volume of the figure enclosed by the curve , the

y

axis and th line

y=b

, revolved around the

y

axis. What's the relation of

U

and

V?

1978 Chuo university entrance exam/Science and Technology

Problem Statement