The area bounded by x + y = 1 and y ≥ x 2 in the first quadrant is a - a 2 2 - a 3 3 sq. units, then the value of 2 a + 1 2 is equal to

Step-by-step solution

For A → 1 - x = x 2 ⇒ x 2 + x - 1 = 0 ⇒ x = - 1 ± 5 2 ⇒ A is - 1 + 5 2 , 3 - 5 2 Thus, the required area is Area = ∫ 0 5 - 1 2 1 - x - x 2 d x = x - x 2 2 - x 3 3 0 5 - 1 2 = a - a 2 2 - a 3 3 where a = 5 - 1 2 ⇒ 2 a + 1 = 5 ⇒ 2 a + 1 2 = 5