This preview shows pages 1–2. Sign up to view the full content.
Friday, November 4
−
Lecture 23 :
The definite integral
(Refers to Section 5.2 in your
text)
Students who have mastered the content of this lecture know about
:
The definition of the definite
integrals, area, net area
Students who have practiced the techniques presented in this lecture will be able to
:
Compute the
definite integral by using its definition.
23.1
Definition – Suppose we are given a continuous function
f
(
x
) over an interval [
a
,
b
]
subdivided into
n
equal subintervals
x
0
=
a
,
x
1
,
x
2
, …,
x
n
−
1
,
x
n
= b
each of length
∆
x = x
i
–
x
i
−
1
. For each subinterval [
x
i
−
1
,
x
i
] let
x
i
* denote the
rightendpoint
. Then
is abbreviated by the expression
This expression is called the
definite integral
of
f
over [
a
,
b
]. When viewed in this
context the numbers
a
and
b
are referred to as the
limits of integration
,
f
(
x
) is referred to
as the
integrand
and “
dx
” as the
differential
. Note that, at this point, the symbol “
dx
”
plays no role in the computation of the value of the definite integral. Many prefer to view
it as a symbol which states explicitly what the variable is in the integrand.
This 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.
 Spring '11
 RobertAndre
 Calculus, Integrals

Click to edit the document details