This region is the intersection of the
following regions A1 = {(x, y) : 0 ≤ y ≤ x2 + 1},
A2 = {(x, y) : 0 ≤ y ≤ x + 1}
and
A3 = {(x, y) : 0 ≤ x ≤ 2}
The points of intersection of y = x2 + 1 and y = x + 1 are points P(0, 1) and Q(1, 2) 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