From the Fig 8 24, the required region is the shaded region OPQRSTO whose area
= area of the region OTQPO + area of the region TSRQT
=
1
2
2
0
1
(
1)
(
1)
x
dx
x
dx
+
+
+
∫
∫
(Why )
Fig 8 24
APPLICATION OF INTEGRALS         375
=
1
2
3
2
1
0
3
2
x
x
x
x








+
+
+
















=
(
)
1
1
1
0
2
2
1
3
2








+
−
+
+
−
+
















 = 23
6
Miscellaneous Exercise on Chapter 8
1