Symbolically, we express
A = 
A
( )
b
b
b
a
a
a
d
ydx
f x dx
=
=
∫
∫
∫
The area A of the region bounded by
the curve x = g (y), y-axis and the lines y  =  c,
y = d is given by
A = 
( )
d
d
c
c
xdy
g y dy
=
∫
∫
Here, we consider horizontal strips as shown in
the Fig 8 2
Remark If the position of the curve under consideration is below the x-axis, then since
f (x) < 0 from x = a to x = b, as shown in Fig 8 3, the area bounded by the curve, x-axis
and the ordinates x = a, x = b come out to be negative But, it is only the numerical
value of the area which is taken into consideration