 ## Book: RD Sharma - Mathematics (Volume 2)

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 49 of Exercise 21.3

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49
##### 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.

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