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

Step-by-step solution

I = ∫ a b f x d x f ( a + b - x ) = f ( x ) I = ∫ - π 2 π 2 1 + sin 2 x 1 + π sin x d x … i I = ∫ - π 2 π 2 1 + sin 2 x 1 + π - sin x d x . . . ii Add equation i and ii 2 I = ∫ - π 2 π 2 1 + sin 2 x d x 2 I = π + 1 2 ∫ - π 2 π 2 1 - cos 2 x d x 2 I = π + 1 2 x - sin 2 x 2 - π 2 π 2 2 I = π + 1 2 π 2 - 0 - - π 2 - 0 2 I = π + 1 2 π 2 I = 3 π 2 ⇒ I = 3 π 4