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 Solution As shown in the Fig 8 21, the line
y = 3x + 2 meets x-axis at x = 
32
−
 and its graph
lies below x-axis for
1, 32
x
−


∈ −



 and above
x-axis for 
32 ,1
x
−

∈


 Fig 8