Dirac delta integrated from 0 to infinity

  • Thread starter 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
 

Char. Limit

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

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

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


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

Then the answer is 0.
 
You get 1/2, Dirac delta is a symmetric function.
 
Depends on which direction you approach 0 from. If your integral is...

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

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


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

Then the answer is 0.
Thanks a lot this makes sense.
 

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