The given equations are,
When y = 0 then x = 0,
Or x = \(\sqrt{6y}\)
Putting x value on y2 = 6x,
When y = 0 then x = 0,
And When y = 6 then x = 6,
On solving these two equations, we get point of intersections.
The points are O (0,0) and A(6,6). These are shown in the graph below
Now the bounded area is the required area to be calculated, Hence,
Bounded Area, A = [Area between the curve (i) and x axis from 0 to 6] - [Area between the curve (ii) and x axis from 0 to 6]
On integrating the above definite integration,
Area of the region bounded by the parabolas y2 = 6x and x2 = 6y is 12sq. units.
