Let the area of the region x , y : 2 x - 1 ≤ y ≤ x 2 - x , 0 ≤ x ≤ 1 be A . Then 6 A + 11 2 is equal to _____ .

Step-by-step solution

Given, The area of the region x , y : 2 x - 1 ≤ y ≤ x 2 - x , 0 ≤ x ≤ 1 be A , Now solving, x - x 2 = 2 x - 1 ⇒ x 2 + x - 1 = 0 ⇒ x = - 1 ± 5 2 And equating x - x 2 = 1 - 2 x , we get x = 3 ± 5 2 Now plotting the diagram of y ≥ 2 x - 1 and y ≤ x 2 - x , Now from diagram, both curve are symmetric about x = 1 2 Hence, area of the bounded region is given by, A = 2 ∫ 3 - 5 2 1 2 x - x 2 - 1 - 2 x d x ⇒ A = 2 ∫ 3 - 5 2 1 2 - x 2 + 3 x - 1 d x &#