The area bounded by y = 1 x and y = 1 2 x - 1 from x = 1 to x = 2 is ln ⁡ a sq. units, then 3 a 2 is equal to

Step-by-step solution

As 1 x > 1 2 x - 1 ∀ x ∈ 1 , 2 ∴ the required area is A = ∫ 1 2 1 x - 1 2 x - 1 d x = ln ⁡ x 1 2 - 1 2 ln ⁡ 2 x - 1 1 2 = ln ⁡ 2 - 1 2 ln ⁡ 3 = ln ⁡ 2 - ln ⁡ 3 = ln ⁡ 2 3 sq. units ∴ a = 2 3 ⇒ 3 a 2 = 4