Let us find the intersection points first, We have the equations of curves,
y = 4x – x2 …….(1)
y = x2 – x ………(2)
From (1) and (2) we can get,
x2 – x = 4x – x2
2x2 – 5x = 0
x(2x – 5) = 0
x = 0 or x = 5/2
Putting these values of x in equation (2) we get,
At x = 0,
Y = 02 – 0 = 0
At x = 5/2
Hence intersection points are (0, 0) and \(\left(\frac{5}{2},\frac{15}{4} \right)\)
Area bounded by the curves is shown by the shaded region of the figure shown above.
Area of Shaded Region = \(\frac{125}{4}\) Square units.