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AP EAMCET2006MathematicsDefinite Integration

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

Options

  1. A0
  2. B1
  3. Ce^2-1 2 e
  4. De^2+2 2 e

Correct answer

C. e^2-1 2 e

Step-by-step solution

I= _ -1 ^1 x 1+e^ 2 x d x= _ -1 ^1 e^x+e^ -x 2 (1+e^ 2 x ) d x ( x= e^x+e^ -x 2 )= 1 2 _ -1 ^1 1+e^ 2 x (1+e^ 2 x ) e^x d x= 1 2 _ -1 ^1 e^ -x d x=- 1 2 [e^ -x ]_ -1 ^1=- 1 2 (e⁻¹-e^1 )= e^2-1 2 e

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