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

To find the area bounded by

y = √x ...(i)


y = x ...(ii)


On solving the equation (i) and (ii),


Or x2 = x


Or, x(x – 1) = 0


Or, x = 0 or x = 1


Then y = 0 or y = 1


Equation (i) represent a parabola with vertex (0,0) and axis as x - axis


Equation (ii) represents a line passing through origin.


Points of intersection are (0,0) and (1,1).


These are shown in the graph below: -



Area of bounded region






The area of the region bounded by y = √x and y = x is


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