)
= 
2
1
4
0
sin
1
0
2
2
b
a
a
a
−




× +
−










= 
2
4
2 2
b a
ab
a
π =π
Fig 8 6
Fig 8 7
APPLICATION OF INTEGRALS         363
Alternatively, considering horizontal strips as
shown in the Fig 8 8, the area of the ellipse is
= 
0
4∫
b xdy  = 
2
2
0
4
−
∫
ab
b
y dy
b
 (Why