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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
Methods of Integration 12-21
Example 12.30 Evaluate sech x dx
0
.
Solution: We know that
sech x
e e
e
e
x x
x
x
=
+
=
+
2 2
1
2
=
+
sech x dx
0
2
0
2
1
e
e
dx
x
x
Let u e du e dx
x x
= =
=
+
=
=
=
sech x dx
0
2
0
1
0
1
0
2
1
2
2
2
u
du u
e
x
tan
tan
[
ttan tan ]
[tan tan ]
= ∞−
=
= =
1 1 0
1 1
2 1
2
2 4
2
4 2
e e
p p p p
..
12.5 INTEGRATION OF TRIGONOMETRIC FUNCTIONS AND THEIR
REDUCTION FORMULAE
In this section, we shall discuss the integration of various trigonometric functions using their reduction
formulae.
Integration of sin
n
x where n is a Positive Integer
There are two cases accordingly whether n is odd or even:
If n is an odd positive integer, the ...
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Publisher Resources

ISBN: 9789353948221