![]() |
[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] |
![]() |
Mathematics-Online lexicon: Annotation to | ||
Riemann Integral |
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |
For a positive function ,
corresponds to the area
below the graph of
.
For a sequence
of partitions with
,
we compare the Riemann sums corresponding to
and
with the aid of a partition
, which consists of the union of the
points of
and
:
![]() |
![]() |
![]() |
|
![]() |
![]() |
||
![]() |
![]() |
The convergence of two sequences to the same limit can be established with an identical argument.
For piecewise continuous , the proof is technically more complicated.
It relies on the uniform continuity of
on the closed interval of
integration:
automatisch erstellt am 22. 9. 2016 |