The vertex of the parabola y2 = 2x is at the origin O = (0, 0).
To find the points of intersection of the line and the parabola, equaling the values of 2x from both the equations we get,
y2 = y
∴ y – y = 0
∴ y = 0 or y = 1
When y = 0, x = 0/2 = 0
When y = 1, x = 1/2
∴ the points of intersection are 0(0, 0) and B(1/2 , 1)
Required area = area of the region OABCO = area of the region OABDO – area of the region OCBDO
Now, area of the region OABDO = area under the parabola y2 = 2x between x = 0 and x = 1/2
Area of the region OCBDO = area under the line y = 2x between x = 0 and x = 1/2