The value of ∫ - π 2 π 2 1 1 + e sin x d x is :

Question

The value of ∫ - π 2 π 2 1 1 + e sin x d x is :, π 4, π, π 2, 3 π 2

MARKS App · Accepted Answer

I = ∫ - π 2 π 2 1 1 + e sin x d x ⇒ I = ∫ - π 2 π 2 1 1 + e sin π 2 - π 2 - x d x = ∫ - π 2 π 2 1 1 + e sin - x d x ⇒ I = ∫ - π 2 π 2 e sin x 1 + e sin x d x Using the property, ∫ a b f x d x = ∫ c b f a + b - x d x 2 I = ∫ - π 2 π 2 1 d x ⇒ I = 1 2 ∫ - π 2 π 2 d x I = 1 2 x - π 2 π 2 ⇒ I = π 2

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