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

The value of the integral ∫-11logx+x2+1dx is:
  1. 2
  2. 0
  3. -1
  4. 1

Solution

Let I=∫-11logx+x2+1dx

Consider fx=logx+x2+1 

Now, f-x=log-x+1+x2

⇒f-x=-logx+1+x2

⇒f-x=-fx

So, fx is an odd function.

∴ I=0

Asked in: JEE Main 2021 (25 Jul Shift 2)

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