The positive value of parameter a for which the area bounded by parabolas y = x - a x 2 and a y = x 2 attains the maximum value is

Step-by-step solution

Points of intersection are at x = 0 ,   a 1 + a 2 A r e a = ∫ 0 a 1 + a 2 x - a x 2 - x 2 a dx = 1 6 . 1 a + 1 a 2 Hence, area is maximum when a = 1 ∵   a + 1 a ≥ 2