MathDB

Today's calculation of Integral 189

Source: Osaka University entrance exam/Science and Engineering 2007

March 3, 2007

calculusintegrationlimitgeometry3D geometrycalculus computations

Problem Statement

Let

n

be positive integers. Denote the graph of

y=\sqrt{x}

C,

and the line passing through two points

(n,\ \sqrt{n})

and

(n+1,\ \sqrt{n+1})

l.

Let

V

be the volume of the solid obtained by revolving the region bounded by

C

and

l

around the

x

axis.Find the positive numbers

a,\ b

such that

\lim_{n\to\infty}n^{a}V=b.