The area bounded by y = ( x 2 - x ) 2 with the x -axis, between its two relative minima, is A sq. units. Then, the value of 15 A is equal to

Step-by-step solution

The given curve is y = x 2 ( x - 1 ) 2 ∴ it has relative minima at x = 0 and x = 1 . Then, the required area is A = ∫ 0 1 x 2 x - 1 2 d x = ∫ 0 1 x 2 - x 2 d x = ∫ 0 1 x 4 + x 2 - 2 x 3 d x = x 5 5 + x 3 3 - x 4 2 0 1 = 1 5 + 1 3 - 1 2 = 1 5 - 1 6 = 1 30 sq. units ∴ 15 A = 1 2