Proving Integrability of Constant Function f on [a,b]

  • Thread starter Thread starter tomboi03
  • Start date Start date
  • Tags Tags
    Constant Function
Click For Summary

Homework Help Overview

The discussion revolves around proving the integrability of a constant function multiplied by another function on the interval [a,b]. The original poster seeks assistance in demonstrating that if a function f is integrable, then the product of a constant c and f is also integrable, along with the relationship between their integrals.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the definitions of integrability and the integral itself, suggesting that revisiting these definitions may provide clarity. There is a mention of considering different cases based on the sign of the constant c, which raises questions about the implications of these cases on the proof.

Discussion Status

The discussion is ongoing, with participants exploring different angles of the problem. Some guidance has been offered regarding the importance of definitions and the potential utility of separating cases based on the value of c. However, there is no explicit consensus on the approach to take.

Contextual Notes

Participants are navigating the definitions of integrability and the integral, indicating that these foundational concepts may be crucial to resolving the problem. The original poster expresses uncertainty about how to proceed, highlighting the exploratory nature of the discussion.

tomboi03
Messages
74
Reaction score
0
Suppose that f is integrable on [a,b]. Let c E [tex]\Re[/tex]. Prove that cf is integrable on [a,b] and that
[tex]\int[/tex] cf= c [tex]\int[/tex] f
(both integrals goes from a to b i didn't kno how to put it in the integral)

I'm not sure how to go about this problem
Please help me out~
Thanks
 
Physics news on Phys.org
When you are completely "stuck", look back to the definitions.

How have you defined [itex]\int_a^b f(x) dx[/itex]?
 
okay, i just got a hint saying that it would be best if we treat this separately with the cases c[tex]\leq[/tex]0 and c[tex]\geq[/tex]0.

how would that help me out? wouldn't it just be the same thing except it will be either negative or positive?
 
How have you defined [itex]\int_a^b f(x)dx[/itex]?
 

Similar threads

Replies
9
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
4
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
20
Views
2K
  • · Replies 105 ·
4
Replies
105
Views
11K
Replies
8
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K