Understanding the Dirac Delta Function: Solving the Integral of Delta(x-b)

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Discussion Overview

The discussion revolves around the integral of the Dirac delta function, specifically the expression ∫ Delta(x-b) dx with limits from negative infinity to a variable upper limit. Participants explore the implications of the integral based on the relationship between the variable b and the upper limit a.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks for help in solving the integral of Delta(x-b) from negative infinity to a, indicating they have attempted the problem but are unsure of the steps involved.
  • Another participant questions the implications of the relationship between a and b, specifically what can be inferred if a < b.
  • A third participant expresses a need for assistance with the first step of the integration, citing a lack of recent practice with integration techniques.
  • A later reply states a fact about the integral of the Dirac delta function, asserting that the integral equals 1 if b is within the limits of integration and 0 otherwise, suggesting this is a fundamental property of the delta function.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are multiple questions and varying levels of understanding regarding the integral and its implications.

Contextual Notes

Some participants express uncertainty about the integration process and the conditions under which the delta function evaluates to 1 or 0, indicating potential gaps in understanding or assumptions about the limits of integration.

Who May Find This Useful

This discussion may be useful for students or individuals seeking clarification on the properties and applications of the Dirac delta function in integrals, particularly in the context of mathematical physics or engineering.

extreme2000
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Q: Integral of Delta(x-b)dx and the lower limit is (-) infinity and upper is a
Please help me in steps tried my best to solve.Note this is not homework I was doing the book problems or my practice
Thanks
 
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What can you tell if [itex]a<b[/itex]?

What about the integral in the whole line?
 
Integral Problem

Dear User
Actually I am sorry to say that my integration is little rusty that's why just I need the first step for this question,Please if you can give it to me
Thanks
 
Fact: [tex]\int_A\delta({x-b})dx=1 \textnormal{ if } b\in{A} \textnormal{ or } 0 \textnormal{ otherwise.}[/tex]

That should be all the information you need. This fact should be fairly obvious to understand, but we can explain it in more detail if needed.
 

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