20, the vertex of the parabola
y2 = 4ax is at origin (0, 0) The equation of the
latus rectum LSL′ is x = a Also, parabola is
symmetrical about the x-axis The required area of the region OLL′O
= 2(area of the region OLSO)
= 
20
∫a ydx
 = 
20
4
a
ax dx
∫
= 
0
2
2
a
a
xdx
×
∫
= 
3
2
0
2
4
3
a
a
x

×






= 
23
8
3
a a








 = 
82
3
a
Example 12 Find the area of the region bounded
by the line y = 3x + 2, the x-axis and the ordinates
x = –1 and x = 1