Proving the Limit of Integrable Functions on a Closed Interval

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Homework Help Overview

The discussion revolves around proving a limit related to integrable functions on a closed interval, specifically focusing on the behavior of the integral as the upper limit approaches a point from the right.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the correct interpretation of the limit involving the integral and question the original poster's phrasing. There is a suggestion to utilize the definition of integrals in terms of Riemann sums, although some participants express unfamiliarity with this concept.

Discussion Status

The discussion is ongoing, with participants clarifying terms and definitions. There is no explicit consensus yet, but guidance has been offered regarding the use of Riemann sums as a potential approach to the problem.

Contextual Notes

One participant notes a lack of familiarity with Riemann sums, which may affect their ability to engage with the suggested approach. The original poster's phrasing of the limit is also questioned for clarity.

tomboi03
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Prove: If f is integrable on [a , b] then
lim f =0
x[tex]\rightarrow[/tex]a+

the integral goes from a to x.

How do i go about and prove this? I'm confused.
Please help me out!
Thank You
 
Last edited:
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Do you mean
[tex]\lim_{x\rightarrow a^+} \int_a^x f(t)dt= 0[/tex]

The way you have written it, that the limit of f is 0, makes no sense- that certainly is not necessarily true.

My suggestion here is the same as to your other question: use the definition of integral in terms of Riemann sums.
 


I've never learn Riemann sum definition.
What is that?
 


First, is what I wrote what you mean. And if you have never learned Riemann sums, what definition of [itex]\int_a^b f(x)dx[/itex] are you using?
 

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