Therefore, the area
A bounded by the curve y = f (x), x-axis and the ordinates x = a and x = b is given
by A = |A1| + A2 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