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Let ∫ d x x 2 + 1 - x = f x + C such that f 0 = 0 and C is the constant of integration, then the value of f 1 is

Options

  1. A1 2 + 1 2 ln ⁡ 1 + 2
  2. B1 2 + 1 2 ln ⁡ 1 + 2
  3. C1 2 + 1 2 ln ⁡ 2 + 1
  4. D1 2 + 1 2 1 + ln ⁡ 1 + 2

Correct answer

D. 1 2 + 1 2 1 + ln ⁡ 1 + 2

Step-by-step solution

∫ x 2 + 1 + x 1 d x ∫ x 2 + 1 d x + ∫ x d x = x 2 x 2 + 1 + 1 2 ln ⁡ x + x 2 + 1 + x 2 2 + C f x = x 2 x 2 + 1 + 1 2 ln ⁡ x + 1 x 2 + 1 + x 2 2 f 0 = 0 f 1 = 2 2 + 1 2 ln ⁡ 1 + 2 + 1 2 = 1 2 + 1 2 1 + ln ⁡ 1 + 2

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