The area bounded by the curves y = cos ⁡ x and y = sin ⁡ 2 x ,   ∀ x ∈ π 6 , π 2 is equal to

Step-by-step solution

A = ∫ π 6 π 2 sin ⁡ 2 x - cos ⁡ x d x = – cos ⁡ 2 x 2 - sin ⁡ x π 6 π 2 = cos ⁡ 2 x 2 + sin ⁡ x π 2 π 6 = 1 2 × 1 2 + 1 2 + 1 2 - 1 = 1 4 sq. units