DiracDelta function example from Wolfram documentation

In summary, the Dirac Delta function, also known as the impulse function, is a mathematical function used in physics and engineering to represent a point or spike of infinite magnitude in a specific location. It is typically defined as zero everywhere except at the origin, where it is infinite. It is represented mathematically by the symbol δ(x) and is used to model situations where a point or spike of infinite magnitude occurs, as well as to simplify mathematical calculations. It is used in practical applications such as signal processing, image processing, and quantum mechanics. However, there are limitations to using this function, as it is an idealized mathematical concept and does not exist in physical reality. It is often approximated in practical applications by a narrow
  • #1
Swamp Thing
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TL;DR Summary
Example of DiracDelta from the Wolfram Language help doesn't seem to work, at least on Wolfram Cloud.
The page on the Wolfram function DiracDelta has this example:
Code:
Integrate[DiracDelta[x] Cos[x], {x, -Infinity, Infinity}]
It's the first example under Examples > Basic Examples. When I run it in Wolfram Cloud, it says "Invalid integration variable or limit(s) ..."
and shows this result:
1577242349659.png


What's going wrong?

Edit: here's a screenshot:
1577242663222.png
 
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  • #2
Have you set x to 3 earlier in your script?
 
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Likes Swamp Thing
  • #3
O... M... G...

Yes, I have, actually :oops:
 
  • #4
Try clearing x or use another integration variable.
 
  • #5
Thanks, it works now.
 

1. What is the Dirac Delta function?

The Dirac Delta function is a mathematical concept that represents an infinitely tall and narrow spike at a specific point on a number line. It is often used in physics and engineering to model point masses or point charges.

2. How is the Dirac Delta function defined?

The Dirac Delta function is defined as a distribution, or generalized function, rather than as a traditional function. It is defined as zero everywhere except at the origin, where it is infinite, and the area under the function is equal to one.

3. What is the significance of the Dirac Delta function in mathematics?

The Dirac Delta function is a fundamental tool in many areas of mathematics, including calculus, differential equations, and Fourier analysis. It allows for the simplification of complex mathematical expressions and the representation of point sources in physical systems.

4. How is the Dirac Delta function used in engineering and physics?

In engineering and physics, the Dirac Delta function is used to model point masses, point charges, and other point sources in physical systems. It is also used in solving differential equations and in Fourier analysis to represent signals and systems.

5. Are there any limitations to using the Dirac Delta function?

Yes, there are limitations to using the Dirac Delta function. It is a mathematical concept and not a physical entity, so it cannot be directly measured or observed. Additionally, it is an idealization and may not accurately represent real-world systems that have finite size and mass.

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