The values of ∫ - π 2 π 2 sin 2 ⁡ x 1 + 2 x d x is

Step-by-step solution

I =   ∫ - π 2 π 2 sin 2 x 1 + 2 x   d x       . . . ( i ) As ∫ a b f ( x ) d x = ∫ a b f ( a + b − x ) d x I = ∫ - π 2 π 2 sin 2 ⁡ - x 1 + 2 - x d x I =   ∫ - π 2 π 2 2 x sin 2 ⁡ x 1 + 2 x d x         . . . ( ii ) By adding Equations ( i ) and ( ii ) , 2 I =   ∫ - π 2 π 2 1 + 2 x sin 2 ⁡ x 1 + 2 x d x 2 I = 2 ∫ 0 π 2 sin 2 ⁡ x d x I = ∫ 0 &