Q36 / 116 · NTA Abhyas (JEE Main) 2020 · Mathematics · Definite Integration

The integral ∫ −1/2 1/2 ( [ x ]+ℓn( 1+x 1−x ) )dx is equal to  (x is the greatest integer ≤x)

  • Correct answer
    A
    − 1 2
  • B
    1
  • C
    2ℓn( 1 2 )
  • D
    0

Solution

Let, I= ∫ −1/2 1/2 ( [ x ]+ℓn( 1+x 1−x ) )dx

= ∫ −1/2 1/2 [ x ]dx+ ∫ −1/2 1/2 ℓn( 1+x 1−x )dx

= ∫ −1/2 0 −1dx+ ∫ 0 1/2 0dx+0                         [ ∵  log( 1+x 1−x )is  an  odd  function ]

=[−x]-1/20=0−(12)=−12

Hence, the correct answer is option: 'A'.

More Definite Integration Questions