Let g x = cos x 2 , f x = x , and α , β α < β be the roots of the quadratic equation 18 x 2 - 9 π x + π 2 = 0 . Then the area (in sq. units) bounded by the curve y = g o f x and the lines x = α , x = β and y = 0 , is

Step-by-step solution

Given, g x = cos x 2 ,   f x = x Given quadratic is 18 x 2 - 9 π x + π 2 = 0 The roots are x = 9 π ± 81 π 2 - 72 π 2 2 × 18 ⇒ x = 9 π ± 9 π 2 36 ⇒ x = 9 ± 3 π 36 ⇒ x = π 3 ,   π 6 y = g o f x = cos x 2 = cos x Required Area = ∫ π 6 π 3 cos ⁡ x   d x = sin x π 6 π 3 ⇒   3 2 - 1 2