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The value of the integral ∫ − a a e x 1 + e x d x is

Options

  1. Ae a 2
  2. Ba
  3. Ce - a 2
  4. Da 2

Correct answer

B. a

Step-by-step solution

∫ − a a e x 1 + e x d x ​ = ∫ 0 a e x 1 + e x + e − x 1 + e − x d x ∵ ∫ − a a f ( x ) d x = ∫ 0 a f ( x ) + f ( − x ) d x = ∫ 0 a e x 1 + e x + 1 1 + e x d x = ∫ 0 a d x = a

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