Verified Solution • 2025–26 Session moderate

QJEEM21Ma7072: JEE Main 2021 Mathematics - Class 12 JEEM21Ma7072 Solution: The value of the integral is :

The value of the

integral ∫−11log⁡(x+x2+1)dx\int\limits_{ - 1}^1 {\log \left( {x + \sqrt {{x^2} + 1} } \right)dx} is :

Multiple Choice Options

  • A 2
  • B 0
  • C −- 1
  • D 1

Step-by-Step Verified Solution

Let I=∫−11log⁡(x+x2+1)dxI = \int\limits_{ - 1}^1 {\log \left( {x + \sqrt {{x^2} + 1} } \right)dx}

∵\because log⁡(x+x2+1)\log \left( {x + \sqrt {{x^2} + 1} } \right) is an odd function

∴\therefore I = 0

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