Question REgarding Reimann integral

  • Context: Graduate 
  • Thread starter Thread starter shehpar
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary

Discussion Overview

The discussion revolves around the Riemann integrability of a piecewise-defined function g on the interval [0,1]. Participants explore the conditions under which g is Riemann integrable and seek to evaluate the integral of g from 0 to 1. The scope includes theoretical aspects of integration and coursework-related inquiries.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant asks whether the function g, defined as g(x)=1 for x in (0,1] and g(0)=0, belongs to R[0,1] and requests evaluation of the integral.
  • Another participant suggests that the original post belongs in the undergraduate coursework section and references posting guidelines.
  • A participant expresses difficulty in locating the undergraduate section of the forum.
  • One reply emphasizes the importance of showing work and suggests considering a suitable partition to address the point of discontinuity at zero.
  • A participant acknowledges the discontinuity at zero and expresses familiarity with upper and lower sums but admits uncertainty about selecting appropriate partitions and proving Riemann integrability.

Areas of Agreement / Disagreement

The discussion reflects a lack of consensus on how to approach the problem, with some participants focusing on procedural aspects while others express uncertainty about the underlying concepts.

Contextual Notes

Participants have not fully resolved the mathematical steps necessary to prove Riemann integrability or the choice of partitions, indicating potential gaps in understanding.

shehpar
Messages
9
Reaction score
0
Let g:[0,1]--[0,1] be defined by g(x)=1 for x belongs to (0,1] and g(0)=0. Prove that g belongs to R[0,1]?
and evaluate integral of g with lower limit 0 and upper limit 1.. I will really appreciate the ansawer. thanks
 
Physics news on Phys.org
This question belongs in the undergraduate coursework section of this site. Also, please see https://www.physicsforums.com/showthread.php?t=94383 on posting guidelines when requesting coursework help.
 
But where to find undergraduate section. I couldn't find. would you please tell me where is that section. thanks
 
It's more important that you show some work. I'll get you started. What is simple but effective partition to choose here? Assuming you understand the basic definitions involved, including what upper and lower sums are, this problem really comes down to understanding how to deal with the point of discontinuity by choosing the right partition.
 
Thanks for reply,I am sure that point of discontinuity is zero here and, I know about upper and lower sum .. I don't know how to choose the right partitions. I wish, I could.. In fact, I really don't know how to prove that something is Remiann integrable
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 9 ·
Replies
9
Views
3K