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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
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 .