APPLICATION OF INTEGRALS         361
Example 1 Find the area enclosed by the circle x2 + y2 = a2 Solution From Fig 8 5, the whole area enclosed
by the given circle
= 4 (area of the region AOBA bounded by
the curve, x-axis and the ordinates x = 0 and
x = a) [as the circle is symmetrical about both
x-axis and y-axis]
= 
40
∫a ydx
 (taking vertical strips)
= 
2
2
40
a
a
−x dx
∫
Since x2 + y2 = a2 gives     y = 
2
2
a
x
±
−
As the region AOBA lies in the first quadrant, y is taken as positive Integrating, we get
the whole area enclosed by the given circle
= 
2
2
2
–1
0
4
sin
2
2
a
x
a
x
a
x
a


−
+




= 
2
1
4
0
sin 1
0
2
2
a
a
−




× +
−








 =  
2
2
4
2
2
a
a


π
 =π

 


 

Fig 8