23
The required area = Area of the region ACBA + Area of the region ADEA
=
2
1
3
2
1
3
(3
2)
(3
2)
x
dx
x
dx
−
−
−
+
+
+
∫
∫
=
2
1
2
2
3
2
1
3
3
3
2
2
2
2
x
x
x
x
−
−
−




+
+
+








 = 1
25
13
6
6
3
+
=
Example 13 Find the area bounded by
the curve y = cos x between x = 0 and
x = 2π Solution From the Fig 8 22, the required
area = area of the region OABO + area
of the region BCDB + area of the region
DEFD Thus, we have the required area
= 
3π
π
2π
2
2
3π
π
0
2
2
cos
cos
cos
xdx
xdx
x dx
+
+
∫
∫
∫
= [
]
[
]
[
]
3
2
2
2
3
0
2
2
sin
sin
sin
x
x
x
π
π
π
π
π
+
+
= 1 + 2 + 1 = 4
Example 13 Prove that the curves y2 = 4x and x2 = 4y
divide the area of the square bounded by x = 0, x = 4,
y = 4 and y = 0 into three equal parts