5
Fig  8 4
362
MATHEMATICS
Alternatively, considering horizontal strips as shown in Fig 8 6, the whole area of the
region enclosed by circle
= 
40
∫a xdy
 = 
2
2
40
a
a
y
dy
−
∫
(Why )
= 
2
2
2
1
0
4
sin
2
2
a
a
y
y
a
y
a
−


−
+




= 
2
1
4
0
sin 1
0
2
a2
a
−




× +
−








= 
2
2
4
a2 2
a
π = π
Example 2 Find the area enclosed by the ellipse 
2
2
2
2
1
x
y
a
b
+
=
Solution From Fig 8