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JEE Main2013MathematicsDefinite IntegrationActual

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

Options

  1. A2
  2. B4
  3. C4

Correct answer

3

Step-by-step solution

I = _ / 2 ^ / 2 ^2 x 1+2^x d x I = _ - / 2 ^ / 2 ^2 x 1+2^ -x d x , by replacing x by aligned & ( 2 - 2 -x ) I & = _ - / 2 ^ / 2 2^x ^2 x 1+2^x d x aligned Adding equations (i) and (ii), we get array rl 2 & I= _ - / 2 ^ / 2 ^2 x d x= 1 2 _ - / 2 ^ / 2 (1- 2 x) d x I & = 1 4 [x+ 2 x 2 ]_ - / 2 ^ / 2 & = 1 4 [ ( 2 + 2 )- (- 2 + (- ) 2 ) ] I & = 1 4 [ 2 + 2 ]= 4 array

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