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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

The value of the integral ∫ - 1 1 d x 1 + x 2 1 + e x is equal to

Options

  1. Aπ 4
  2. Bπ 2
  3. Cπ
  4. D0

Correct answer

A. π 4

Step-by-step solution

Let, I = ∫ - 1 1 d x 1 + x 2 1 + e x As, ∫ - a a f x d x = ∫ 0 a f x + f - x d x So, I = ∫ 0 1 1 1 + x 2 1 1 + e x + 1 1 + e - x d x ⇒ I = ∫ 0 1 1 1 + x 2 = tan - 1 x 0 1 = π 4

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