The area bounded by f x = s i n 2 x and the x -axis from x = a to x = b , where f " a = f " b = 0 ( ∀ a , b ∈ 0 , π) , is

Step-by-step solution

f " x = 2 cos ⁡ 2 x = 0 ⇒ 2 x = π 2 ,   3 π 2 ⇒ x = π 4 ,   3 π 4 Hence, required area = ∫ π 4 3 π 4 s i n 2 x d x = ∫ π 4 3 π 4 1 - cos ⁡ 2 x 2 d x = x 2 - sin ⁡ 2 x 4 π 4 3 π 4 = π + 2 4