3.25: Shaded area between chord and curve

0606/13/M/J/25 — Question 8 · 8 marks · Log laws, Equations

The diagram shows part of the curve

y = \dfrac{3}{x + 1} - \dfrac{x - 2}{x}

. The points

A

and

B

lie on the curve such that the

x

-coordinate of

A

1

and the

x

-coordinate of

B

2

(a)

Find the

y

-coordinates of

A

and

B

[1]

(b)

Show that the area of the shaded region enclosed by the line

AB

and the curve is

\ln\dfrac{a}{b}

, where

a

and

b

are integers to be found.

[7]