Solution The point of intersection of these two
parabolas are O (0, 0) and A (1, 1) as shown in
the Fig 8 15 Here, we can set y 2 = x or y =
x = f(x) and y = x2
= g(x), where, f (x) ≥ g (x) in [0, 1] Therefore, the required area of the shaded region
= 
[
]
1
0
( )
( )
f x
g x
dx
−
∫
= 
1
2
0
x
x
dx


−


∫
1
3
3
2
0
32
x3
x


=
−






= 
2
1
1
3
3
3
−
=
Example 7 Find the area lying above x-axis and included between the circle
x2 + y2 = 8x and inside of the parabola y2 = 4x