Find the area bounded by the curve x2 = 4y and the line x = 4y – 2.


It is given that the area of the region bounded by the parabola x2 = 4y and x = 4y - 2.


Let A and B be the points of intersection of the line and parabola.


Coordinates of point A are


Coordinates of point B are (2, 1).


Now, draw AL and BM perpendicular to x axis.


We can see that


Area OBAO = Area OBCO + Area OAC) …(1)


Now, Area OBCA = Area OMBC – Area of OMBO




.




Similarly,


Area OACO = Area OLAC – Area of OLAO







Therefore, the required area is


10