Integral of dirac delta function at x=0

In summary, The delta function is not a function and cannot be evaluated at a specific value. However, the integral of the delta function from negative infinity to positive infinity is equal to 1.
  • #1
vsravani
1
0
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
 
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  • #2
Yes.
 
  • #3
vsravani said:
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.
 
  • #4
vsravani said:
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 [tex]\delta(x)[/tex] is not a function, so you can't evaluate it at [tex]x=0[/tex] and write [tex]\delta(0)[/tex]. Maybe you meant

[tex]\int_{-\infty}^{+\infty}\delta(x)dx=1[/tex]

this is correct. Instead

[tex]\int_{-\infty}^{+\infty}\delta(0)dx[/tex]

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

FAQ: Integral of dirac delta function at x=0

What is the integral of dirac delta function at x=0?

The integral of dirac delta function at x=0 is equal to 1. This means that when the dirac delta function is integrated over an interval containing x=0, the result will be 1.

What does the dirac delta function represent in terms of area under the curve?

The dirac delta function represents an infinitely tall and narrow spike at x=0. The area under this spike is equal to 1, which is the integral of the dirac delta function at x=0.

Why is the integral of dirac delta function at x=0 equal to 1?

This is because the dirac delta function is defined as 0 everywhere except at x=0, where it is defined as infinity. The integral is a measure of the area under the curve, and since the dirac delta function has an infinite value at x=0, the area under the curve is equal to 1.

Can the integral of dirac delta function at x=0 have a value other than 1?

No, the integral of dirac delta function at x=0 will always have a value of 1. This is because the dirac delta function is a mathematical construct with a specific definition, and the integral at x=0 is an integral of that construct.

How is the integral of dirac delta function at x=0 used in real-world applications?

The dirac delta function and its integral at x=0 are used in various fields of science and engineering, such as signal processing, quantum mechanics, and fluid dynamics. It is a useful tool for representing impulses or point sources, and its integral at x=0 is often used in calculations and equations to simplify and solve problems.

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