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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
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
Applications of Integration 15-37
=
p ( ( ))f x dx
a
b
2
Therefore, the volume of the solid of revolution generated by
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Publisher Resources

ISBN: 9789353948221