Integral of dirac delta function at x=0

[vsravani]

Hi

Can somebody help me with this...
Is is correct to say that, Integral(delta(0)) = 1 (limits are from -infinity to +infinity)
I don't know latex and sorry for the inconvenience in readability.

Thanks,
VS

 

[JeSuisConf]

Yes.

 

[mathman]

Hi

Can somebody help me with this...
Is is correct to say that, Integral(delta(0)) = 1 (limits are from -infinity to +infinity)
I don't know latex and sorry for the inconvenience in readability.

Thanks,
VS

Examine the definition of the delta function. You will see that yes is the obvious answer.

 

[Petr Mugver]

Hi

Can somebody help me with this...
Is is correct to say that, Integral(delta(0)) = 1 (limits are from -infinity to +infinity)
I don't know latex and sorry for the inconvenience in readability.

Thanks,
VS

The $$\delta(x)$$ is not a function, so you can't evaluate it at $$x=0$$ and write $$\delta(0)$$. Maybe you meant

$$\int_{-\infty}^{+\infty}\delta(x)dx=1$$

this is correct. Instead

$$\int_{-\infty}^{+\infty}\delta(0)dx$$

is meaningless, so in particular it's not 1.