If A = ∫ 0 π 2 sin 3 ⁡ x 1 + cos 2 ⁡ x d x and B = ∫ 0 π 2 cos 3 ⁡ x 1 + sin 2 ⁡ x d x , then 2 A B is equal to

Step-by-step solution

In A , let cos ⁡ x = t ⇒ - sin ⁡ x d x = d t ∴ A = - ∫ 1 0 1 - t 2 1 + t 2 d t = ∫ 0 1 1 - t 2 1 + t 2 d t In B , let sin ⁡ x = u cos ⁡ x d x = d u ∴ B = ∫ 0 1 1 - u 2 1 + u 2 d u = A ∴ 2 A B = 2