The area bounded by the curve y = x (3 – x)2, the x – axis and the ordinates of the maximum and minimum points of the curve is

2 sq. units 6 sq. units 4 sq. units 8 sq. units

4 sq. units

y = x (3 – x)2 After solving , we get x =1 and x = 3 are points of maximum and minimum respectively. Now the shaded region is the required region ∴ $A=\int\limits_1^3 x(3-x)^2 d x$ = 4 sq. units