Dirac delta integrated from 0 to infinity

[Heimisson]

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]

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.

 

[peteratcam]

You get 1/2, Dirac delta is a symmetric function.

 

[Char. Limit]

You get 1/2, Dirac delta is a symmetric function.

It's not even really a function...

 

[Heimisson]

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.