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MHT CET2011MathematicsDefinite Integration

_ - / 2 ^ - / 2 x 1+e^ x d x is equal to

Options

  1. A1
  2. B0
  3. C-1
  4. DNone of these

Correct answer

A. 1

Step-by-step solution

I= _ - / 2 ^ / 2 x 1+e^ x d x aligned I &= _ - / 2 ^ / 2 ( / 2- / 2-x) 1+e^ ( / 2- / 2-x) d x &= _ - / 2 ^ / 2 (-x) 1+e^ -x d x I &= _ - / 2 ^ / 2 x 1+e^ -x d x &= _ - / 2 ^ / 2 e^ x x 1+e^ x d x aligned On adding Eqs. (i) and (ii), we get aligned 2 I &= _ - / 2 ^ / 2 (1+e^ x ) x (1+e^ x ) d x &= _ - / 2 ^ / 2 x d x &=2 ₀^ / 2 x d x aligned [Since, x is an even function.] 2 I=2[ x]₀^ / 2 =2(1-0)=2 I=1

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