If f x is a continuous function satisfying f x = f 2 - x , then the value of the integral I = ∫ - 3 3 f 1 + x ln ⁡ 2 + x 2 - x d x is equal to

Question

If f x is a continuous function satisfying f x = f 2 - x , then the value of the integral I = ∫ - 3 3 f 1 + x ln ⁡ 2 + x 2 - x d x is equal to, 3 π, 6 π, 0, 9 π

MARKS App · Accepted Answer

As f x = f 2 - x Puting x → x + 1 , we get, f x + 1 = f 1 - x Applying a + b - x property in I , we get, I = ∫ - 3 3 f 1 - x ln ⁡ 2 - x 2 + x d x ⇒ I = - ∫ - 3 3 f 1 + x ln ⁡ 2 + x 2 - x d x ⇒ I = - I ⇒ I = 0

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