
15-36 Calculus – Differentiation and Integration
Now, let us find the volume of the ith disk. For this let Dx
i
be the thickness of the ith disk and f(x
i
)
be its radius.
Then the volume of the ith cylindrical disk is p( ( )) .f x x
i i
2
D
Therefore, the volume of solid of revolution is given by
V f x x
f x x
f x
n
i i
n
x
x b
x a
=
∑
=
∑
=
→∞
=
∞
→
=
=
lim ( ( ))
lim ( ( ))
( ( ))
p
p
p
2
1
0
2
∆
∆
∆
22
dx
a
b
∫
Figure 15.19
y
x
a b
y = f(x)
Figure 15.20
y = f(x)
a
b
x
y