WOLFRAM|DEMONSTRATIONS PROJECT

Napier's Inequality (II)

a

0.5

b

1.5

Napier's inequality: If

0<a<b,

then

1

b

<

lnb-lna

b-a

<

1

a

.

Observe that in the graphic,

b

∫

a

1

x

dx

, the area under the curve

y=

1

x

on the interval

(a,b)

, is between the red and blue areas.