Dirac delta integrated from 0 to infinity

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Discussion Overview

The discussion revolves around the integration of the Dirac delta function from 0 to infinity, specifically when integrated with the constant function 1. Participants explore the implications of the limits of integration and the properties of the Dirac delta function.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether the integral of the Dirac delta function from 0 to infinity results in 0.5 or 1, expressing uncertainty based on a previous class discussion.
  • Another participant suggests that the result depends on the direction from which 0 is approached, indicating that approaching from the left yields 1 and from the right yields 0.
  • Some participants assert that the result is 1/2, citing the symmetry of the Dirac delta function.
  • There are multiple reiterations of the same points, with some participants emphasizing that the Dirac delta is not a conventional function.

Areas of Agreement / Disagreement

Participants express differing views on the result of the integral, with some advocating for 1/2 due to symmetry, while others argue that the result depends on the approach to 0, leading to 1 or 0. No consensus is reached.

Contextual Notes

The discussion highlights the ambiguity in defining the limits of integration and the nature of the Dirac delta function, which may affect the interpretation of the integral's value.

Heimisson
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I was wondering if I integrate the dirac delta function from 0 to infinity where the function it's integrated with is the constant 1, will I get 0.5 or 1? And why?

This is not homework so I decided to post this here although I asked this question in class and the teacher (assistant) wasn't too sure. I could ask my professor but he's a scary man and mocks your questions.

So I was hoping someone here could answer this.

thanks
 
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Heimisson said:
I was wondering if I integrate the dirac delta function from 0 to infinity where the function it's integrated with is the constant 1, will I get 0.5 or 1? And why?

This is not homework so I decided to post this here although I asked this question in class and the teacher (assistant) wasn't too sure. I could ask my professor but he's a scary man and mocks your questions.

So I was hoping someone here could answer this.

thanks

Depends on which direction you approach 0 from. If your integral is...

lim_{a\rightarrow{0^-}} \int_a^\infty \delta(x) dx

Then the answer is 1. If your integral is...


lim_{a\rightarrow{0^+}} \int_a^\infty \delta(x) dx

Then the answer is 0.
 
You get 1/2, Dirac delta is a symmetric function.
 
peteratcam said:
You get 1/2, Dirac delta is a symmetric function.

It's not even really a function...
 
Char. Limit said:
Depends on which direction you approach 0 from. If your integral is...

lim_{a\rightarrow{0^-}} \int_a^\infty \delta(x) dx

Then the answer is 1. If your integral is...


lim_{a\rightarrow{0^+}} \int_a^\infty \delta(x) dx

Then the answer is 0.

Thanks a lot this makes sense.
 

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