Equations of above mentioned curves will be
in their standard forms only as the cases in other forms go beyond the scope of this
textbook Example 3 Find the area of the region bounded
by the curve y = x2 and the line y = 4 Solution Since the given curve represented by
the equation y = x2 is a parabola symmetrical
about y-axis only, therefore, from Fig 8 9, the
required area of the region AOBA is given by
4
20
∫xdy
 =
areaof theregionBONB boundedbycurve,
axis
2 andthelines
0and
= 4
y
y
y
−




=


= 
4
20
ydy
∫
 = 
4
3
2
0
2
2
3
y


×






 
4
32
8
3
3
=
×
=
(Why