The area (in sq. units) bounded by y = max ⁡ sin 2 ⁡ x , sin 4 ⁡ x , x ∈ 0 , π 2 with the x -axis, from x = 0 to x = π 2 is

Step-by-step solution

As x ∈ 0, π 2 , sin ⁡ x ∈ 0 , 1 ⇒ sin 2 ⁡ x > sin 4 ⁡ x So, the required area is A = ∫ 0 π 2 sin 2 ⁡ x d x = ∫ 0 π 2 1 - cos ⁡ 2 x 2 d x = x 2 - sin ⁡ 2 x 4 0 π 2 = π 4 - 0 - 0 - 0 = π 4 sq. units