RD Sharma - Mathematics (Volume 2)

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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