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