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In what ratio does the x-axis divide the area of the region bounded by the parabolas y = 4x – x2 and y = x2 – x?
Let us find the intersection points first,
We have the equations of curves,
y = 4 x – x2 …….(1)
y = x2 – x ………(2)
From (1) and (2) we can get,
x2 – x = 4 x – x2
2 x2 – 5x = 0
x(2 x – 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
Area bounded by the curves is shown by the shaded region of the figure shown above.
Area of shaded region =
Area of shaded region =
Area of Shaded Region =
Area of Shaded Region = Square units.