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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

Options

  1. A3 π
  2. B6 π
  3. C0
  4. D9 π

Correct answer

C. 0

Step-by-step solution

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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