This preview shows pages 1–9. Sign up to view the full content.
Tuesday, January 10
−
Lecture 4
:
More Integration Methods : Trigonometric
Substitution
(
Refers to Section 6.4 in your text
)
After having practiced the problems associated to the concepts of this lecture the student
should be able to
:
Solve integrals of functions containing
a
2
−
x
2
,
a
2
+
x
2
or
x
2
−
a
2
by applying an appropriate trig substitution, solve definite integrals by trig substitution.
4.1
The method called “Trigonometric substitution”
−
This method applies to integrands
containing
a
2
−
x
2
,
a
2
+
x
2
or
x
2
−
a
2
. It is summarized in the following table:
Note
−
The restriction
x
=
a
sec
θ,
0
≤ θ < π
/2,
π
≤ θ <
3
π
/2 is due to the way
θ
=
arcsec
y
is defined. That is,
θ
= arcsec
y
if and only if sec
θ
=
y
and
θ ∈
[0,
π
/2)
∪
[
π
, 3
π
/2).
The definition is not universal. But the important point is
that inverse of trigonometric
functions are defined on intervals where the function is onetoone
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 04/01/2012 for the course MATH 118 taught by Professor Zhou during the Winter '08 term at Waterloo.
 Winter '08
 ZHOU
 Calculus, Integrals

Click to edit the document details