Given curves are
x2 = 4y.....(i)
and x = 4y - 2 ...(ii)
Obviously, curve (i) is a parabola with vertex at (0, 0) and along +ve direction of y-axis, while equation (ii) represents a straight line.
For points of intersection, we solve (i) and (ii) as
Hence, coordinates of intersection points of line and parabola are (-1, \(\frac 14\)) and (2, 1).
Shaded region is region region.
\(\therefore\) Required area = area of trap. ABCD - area of ABOCDOA