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JEE Main20205 Sep 2020Morning ShiftMathematicsDefinite IntegrationActual

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

Options

  1. Aπ 4
  2. Bπ
  3. Cπ 2
  4. D3 π 2

Correct answer

C. π 2

Step-by-step solution

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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