The area (in sq. units) bounded by y = 2 x and y = 2 x - x 2 from x = 1 to x = 2 is k log 2 e - l , then the value of k l is equal to

Step-by-step solution

Required area is A = ∫ 1 2 2 x - 2 x - x 2 d x = 2 x ln ⁡ 2 - x 2 + x 3 3 1 2 = 4 ln ⁡ 2 - 4 + 8 3 - 2 ln ⁡ 2 - 1 + 1 3 = 2 ln ⁡ 2 - 3 + 7 3 = 2 ln ⁡ 2 - 2 3 = 2 l o g 2 e - 2 3 ∴ k = 2 & l = 2 3 ⇒ k l = 3