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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),
y2 = 2y + 3
Or, y2 – 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