Re: Riemann sum with variable interval widths?


C6L1V@xxxxxxx wrote:
G Patel wrote:
C6L1V@xxxxxxx wrote:
G Patel wrote:
Must Riemann sums have fixed interval widths, or can they have
variable?

They can be variable. The general definition involves more-or-less
arbitrary partitions, whose maximum interval lengths go to zero.


That's if we take the limit of Riemann sums for the purpose of finding
the definite integral, right? Riemann sum itself is not a limit. Am I
mistaken?

No, you are right. A Riemann integral is the limit of Riemann sums.
Riemann sums can have variable-width partitions. However, in numerical
analysis, for example, it is most common to use fixed-width intervals
for getting numerical approximations to integrals.


Thanks RGV.

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