)
= 
4
2
2
2
–1
0
32
1
4
4
sin
3
2
2
4
t
t
t


+
−
+
×
×




= 
2
–1
32
4
1
0
4
sin 1
3
2
2


+
×
+
×
×




32
32
0
8
4
3
2
3
π


=
+
+
×
=
+ π




 = 4(8 3 )
3
+ π
Example 8 In Fig 8 17, AOBA is the part of the ellipse 9x2 + y2 = 36 in the first
quadrant such that OA = 2 and OB = 6 Find the area between the arc AB and the
chord AB Solution Given equation of the ellipse 9x2 + y2 = 36 can be expressed as 
2
2
1
4
36
x
+y
=  or
2
2
2
2
1
2
6
x
+y
= and hence, its shape is as given in Fig 8