# 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

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#### Char. Limit

Gold Member
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...

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

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

#### peteratcam

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

#### Char. Limit

Gold Member
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...

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

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

Thanks a lot this makes sense.

"Dirac delta integrated from 0 to infinity"

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