The area bounded by the curve y = sin - 1 ⁡ sin ⁡ x and the x -axis from x = 0 to x = 4 π is equal to the area bounded by the curve y = cos - 1 ⁡ cos ⁡ x and the x -axis from x = - π to x = a , then the value of a is equal to

Step-by-step solution

Graph of y = sin - 1 ⁡ sin ⁡ x Area = 4 × 1 2 × π × π 2 = π 2 Graph of y = c o s - 1 cos ⁡ x is Given, π 2 = 1 2 × π × π + 1 2 × a × a π 2 2 = a 2 2 ⇒ a = π