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If the integral I = ∫ x x - 3 x + 3 x - 1 x - 2 x + 1 d x = f x + C (where, x > 0 and C is the constant of integration) and f 1 = - 1 3 , then the value of f 9 is equal to

Options

  1. A3
  2. B6
  3. C9
  4. D12

Correct answer

C. 9

Step-by-step solution

Given integral is I = ∫ x - 1 3 x - 1 2 d x = ∫ x - 1 d x = 2 3 x 3 2 - x + C ∴ f x = 2 3 x 3 2 - x ⇒ f 9 = 18 - 9 = 9

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