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JEE Main202125 Jul 2021Evening ShiftMathematicsDefinite IntegrationActual

The value of the integral ∫ - 1 1 log x + x 2 + 1 d x is:

Options

  1. A2
  2. B0
  3. C- 1
  4. D1

Correct answer

B. 0

Step-by-step solution

Let I = ∫ - 1 1 log x + x 2 + 1 d x Consider f x = log x + x 2 + 1 Now, f - x = log - x + 1 + x 2 ⇒ f - x = - log x + 1 + x 2 ⇒ f - x = - f x So, f x is an odd function. ∴   I = 0

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