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

Question

The value of the integral ∫ - 1 1 d x 1 + x 2 1 + e x is equal to, π 4, π 2, π, 0

MARKS App · Accepted Answer

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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