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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
Integration 11-31
= =
=
sin
.
1
2
0
1
1
2
1
2
p
pdx
x
Example 11.29 Examine the improper integral
1
3
2
5
x
dx
.
Solution:  The integrand 1/x
3
is not continuous at x = 0. So, we split the given integral up to that point.
That is,
1 1 1
3
2
5
3
2
0
3
0
5
x
dx
x
dx
x
dx
=
+
.
Now, we evaluate each of these integrals as h ® 0.
1 1
1
2
3
2
0
0
3
2
0
0
2
2
x
dx
x
dx
x
h
h
h
h
h
+
=
=
=
lim
lim
lim
00
2
1
2
1
8
+
= −∞
h
.
Hence, the integral is not convergent.
Thus, we need not find
1
3
0
5
x
dx
ò
. Therefore,
1
3
2
5
x
dx
is divergent.
11.3.3 Tests for Convergence of Infinite Integrals
Sometimes the fundamental theorem of Calculus proves to be ineffective in evaluating the infinite
integrals. ...
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Publisher Resources

ISBN: 9789353948221