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 x^{2} = 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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