A continuous function f x is such that f 3 x = 2 f x , ∀ x ∈ R . If ∫ 0 1 f x d x = 1 , then ∫ 1 3 f x d x is equal to

Step-by-step solution

Given, f 3 x = 2 f x Also, ∫ 0 1 f x d x = 1 ⇒ 1 2 ∫ 0 1 f 3 x d x = 1 Substituting, 3 x = t ,   d x = d t 3 , we get, 1 6 ∫ 0 3 f t d t = 1 ⇒ ∫ 0 3 f t d t = 6 ⇒ ∫ 0 1 f t d t + ∫ 1 3 f t d t = 6 ⇒ ∫ 1 3 f t d t = 6 - 1 = 5