From the Fig 8 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