Definition.
Let
f
be a function which is continuous on the closed interval
[a, b]
. The
definite integral of f from a to b
is defined to be the limit
where
is a Riemann Sum of
f
on
[a, b]
.
Comments on the definition.
Example of a definite integral.
[
Using Flash
] [
Using Java
]
Definite integrals and areas.
Properties of definite integrals:
Discussion [
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] [
Using Java
]
if
c
is a constant.
Discussion [
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] [
Using Java
]
Discussion [
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] [
Using Java
]
Discussion [
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] [
Using Java
]
If
0
<
f(x)
<
g(x)
for all
x
in
[a, b]
, then
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] [
Using Java
]
Discussion.
If
a < b
then it is convenient to define
.
How to use Maple to evaluate a definite integral using the definition
.
How to use Derive to evaluate a definite integral using the definition
.
A complicated example of evaluating definite integrals using the definition
.