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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

If f x satisfies f x + f 3 - x = 3 ∀ x ∈ R , then the value of integral I = ∫ 3 4 9 4 f f x d x is equal to

Options

  1. A3
  2. B6
  3. C9 4
  4. D9 2

Correct answer

C. 9 4

Step-by-step solution

Applying a + b - x property and adding, we get, 2 I = ∫ 3 4 9 4 f f x + f f 3 - x d x = ∫ 3 4 9 4 f f x + f 3 - f x d x = ∫ 3 4 9 4 f λ + f 3 - λ d x = ∫ 3 4 9 4 3 d x ⇒ 2 I = 3 9 4 - 3 4 ⇒ I = 9 4

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