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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
14-26  Calculus – Differentiation and Integration
Let x a t x
2 2 2 2
= .
Then x
a
t
x dx
a
t
t dt
2
2
2
2
2 2
1 1
=
=
( )
.
Thus,
x
x a
dx
x
t x
a
t
t dt
a
x t t
2
2 2 3 2 2 2 3 2
2
2 2
2
2 2 2
1
1
1
( ) ( ) ( )
( )
/ /
=
=
22
2
2
2 2 2 2
2 2
2 2
1 1
1
1
1
1 1
1
dt
a
t
a t t
dt
t t
dt
t t
=
=
= +
( )
( )

= +
∫∫
=
+
+
=
+
dt
t
dt
t
dt
t
t
t
c
x
x a
x x
1 1
1
1 1
2
1
1
1
2
2 2
2 2
2
log
log
−−
+
+
a
x x a
c
2
2 2
.
S u m mARy
There are various techniques to integrate the irrational function.
Irrational function can be integrated by the techniques of trigonometric transformations.
There is a method to deal with the integrals of the form ax bx c
2
+ + ,
1
2
ax bx c+ +
and
Ax B
ax bx c
+
+ +
2
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Publisher Resources

ISBN: 9789353948221