The maximum area (in sq. units) bounded by y = sin ⁡ x , y = a x   ∀ a ∈ 1 , 4 and the line π - 2 x = 0 is

Step-by-step solution

The area bounded is maximum if slope of the line y = a x is greatest, i.e. 4 . Hence, the required area = ∫ 0 π 2 4 x - sin ⁡ x d x = 2 x 2 + cos ⁡ x 0 π 2 = π 2 2 + 0 - 0 + 1 = π 2 2 - 1 sq. units