To area enclosed by

Y = 4x – x² (1)

4x – x² = x² – x

2x² – 5x = 0

x = 0 or x =

y = 0 or y =

And y = x² – x

…(2)

Equation (1) represents a parabola downward with vertex at (2,4) and meets axes at (4,0), (0,0).

Equation (2) represents a parabola upward whose vertex is and meets axes at Q(1,0), (0,0).Points of intersection of parabolas are O (0,0) and A .

These are shown in the graph below:

Required area = Region OQAP

The area enclosed by the parabolas y = 4x – x² and y = x² – x is .