If the function f x is symmetric about the line x = 3 , then the value of the integral I = ∫ - 2 8 f x f x + f 6 - x d x is

Step-by-step solution

As f x is symmetric about x = 3 , we get, f 3 + x = f 3 - x Replacing x by 3 - x , we get, f 6 - x = f x Now, using a + b - x property in I , and adding, we get, ⇒ 2 I = ∫ - 2 8 f x + f 6 - x f x + f 6 - x d x ⇒ 2 I = ∫ - 2 8 1 d x = x - 2 8 ⇒ 2 I = 10 ⇒ I = 5