RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 3 of Exercise 21.3

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3

Find the area of the region bounded by y = √x and y = x

The given equations are,



And y = x ...(ii)


Solving equation (i) and (ii)


= x = y


Or = y


Or y(y – 1) = 0


So, y = 0 or y = 1 and x = 0 or x = 1


On solving these two equations, we get the points of intersection.


The points are O (0, 0) and A(1,1). These are shown in the graph below



Now the bounded area is the required area to be calculated,


Hence, Bounded Area, A = [Area between the curve (i) and x axis from 0 to 1] - [Area between the curve (ii) and x axis from 0 to 1]




On integrating the above definite integration,







Area of the region bounded by and Y = X is.


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