16, the required area of
the region OPQCO included between these
two curves above x-axis is
= (area of the region OCPO) + (area of the region PCQP)
= 
4
8
0
4
ydx
ydx
+
∫
∫
= 
4
8
2
2
0
4
2
4
(
4)
x dx
x
dx
+
−
−
∫
∫
   (Why )
Fig 8 15
APPLICATION OF INTEGRALS         369
= 
4
3
4
2
2
2
0
0
2
2
4
, where,
4
3
x
t dt
x
t


×
+
−
−
=






∫
(Why )
= 
4
2
2
2
–1
0
32
1
4
4
sin
3
2
2
4
t
t
t


+
−
+
×
×




= 
2
–1
32
4
1
0
4
sin 1
3
2
2


+
×
+
×
×




32
32
0
8
4
3
2
3
π


=
+
+
×
=
+ π




 = 4(8 3 )
3
+ π
Example 8 In Fig 8