Find the area of the region bounded by by y = √x and x = 2y + 3 in the first quadrant and x - axis.

To find an area in the first quadrant enclosed by the x - axis

y = √x ...(i)

x = 2y + 3 ...(ii)

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

y^{2} = 2y + 3

Or, y^{2} – 2y – 3 = 0

Or, (y – 3)(y + 1) = 0

Or, y = 3 or y = – 1

These are shown in the graph below: -

Required area of the bounded region

The area of the region bounded by by y = √x and x = 2y + 3 is

18