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KCET2020MathematicsArea Under Curves

The value of _ - / 2 ^ / 2 x 1+e^ x d x is

Options

  1. A2
  2. B0
  3. C1
  4. D-2

Correct answer

C. 1

Step-by-step solution

We have, _ - / 2 ^ / 2 x 1+e^ x d x= ₀^ / 2 ( x 1+e^ x + (-x) (1+e^ -x ) ) d x [ _ -a ^ a f(x) d x= ₀^ a (f(x)+f(-x)) d x ]= ₀^ / 2 ( x 1+e^ x + e^ x x 1+e^ x ) d x= ₀^ / 2 x ( 1+e^ x 1+e^ x ) d x= ₀^ / 2 x d x=( x)₀^ / 2 = ( 2 - 0 )=1

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