If I = 2 π ∫ - π 4 π 4 d x 1 + e s i n x 2 - c o s 2 x then find 27 I 2 equals____

Step-by-step solution

I = 2 π ∫ - π 4 π 4 1 1 + e s i n x 2 - c o s 2 x ⋅ d x Using ∫ - a a f x ⋅ d x = ∫ 0 a f x + f - x ⋅ d x I = 2 π ∫ 0 π 4 1 1 + e s i n x 2 - c o s 2 x + 1 1 + e - s i n x 2 - c o s 2 x ⋅ d x I = 2 π ∫ 0 π 4 1 1 + e s i n x 2 - c o s 2 x + e s i n x e s i n x + 1 2 - c o s 2 x ⋅ d x I = 2 π ∫ 0 π 4 d x 2 - c o s 2 x I = 2 π ∫ 0 π 4 d x 2 - 1 - t a n 2 x 1 + t a n 2 x = 2 π ∫ 0 &#