Question

Area bounded by the curve 7xy - 7x - 7y - 2 = 0, X-axis and the lines x = 2, x = 3 is ______.

Options

• `1 - 7/9` log 2 sq. units

• `1 + 7/9` log 2 sq. units

• `1 - 9/7` log 2 sq. units

• `1 - 9/7` log 2 sq. units

Answer 1

`1 - 9/7` log 2 sq. units.

Explanation:

7xy - 7x - 7y - 2 = 0

⇒ y(7x - 7) = 7x + 2

⇒ y = `(7"x" + 2)/(7"x" - 7)`

∴ Required area = `int_2^3 "y"  dx = int_2^3 (7"x" + 2)/(7"x" - 7)`dx

`= [x + 9/7 log ("7x" - 7)]_2^3`

= `1 - 9/7` log 2 sq. units.