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

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 .


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