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thanks . I already know this property and many others (including the one in this new attached picture) . If I apply that rule (image) , i would get 1 in the first integral while many others told me 0 . I have problem with the first 2 integrals only .RUber said:The dirac delta function has the great property that ##\int_{-\infty}^{\infty} \delta(x) dx = 1 ##.
Couple that with what you know about when it is not equal to zero, and these integrals are quick and easy.
In the future, please put a little more meat into you post, so we can better understand what you already know and what you need help fixing.
RUber said:Using the rule you attached, you should get 1 in the first integral. What about the second?
It is a Chegg solution . And it confused me .Matterwave said:Where did you get that image? That is not how the Dirac Delta is defined...
Legend101 said:It is a Chegg solution . And it confused me .
I believe that the first integral should be 1 , i just need more proof
No worries . I showed my efforts in attached fileMark44 said:@Legend101, if you start another thread with no effort shown, it will be deleted.
You need to show what you have tried in the first post of the thread. And it would be better to include the work directly in the post, rather than an image of the work.Legend101 said:No worries . I showed my efforts in attached file
The work involves many integrals and mathematical notations . It would be hard to show all the work directly written on the post especially if someone is using a smartphone .Mark44 said:You need to show what you have tried in the first post of the thread. And it would be better to include the work directly in the post, rather than an image of the work.
See my post in that thread.Legend101 said:The work involves many integrals and mathematical notations . It would be hard to show all the work directly written on the post especially if someone is using a smartphone .
A Dirac Delta generalized function, also known as the Dirac delta function, is a mathematical concept used in physics and engineering to represent an idealized point of infinite density and zero width. It is often used to model point particles or to describe the distribution of point charges in an electric field.
Dirac Delta generalized functions are used in integrals to simplify calculations and provide a way to handle discontinuous or singular functions. They allow for the representation of a point source or impulse in a mathematical expression, which can be useful in various physical and engineering applications.
The Dirac Delta generalized function is defined as a distribution, rather than a traditional function, and is represented by the symbol δ(x). Its mathematical definition is given by the following properties:
where f(x) is a continuous function.
No, Dirac Delta generalized functions cannot be integrated in the traditional sense. They are not defined at a single point and do not have a definite value, making traditional integration techniques invalid. Instead, they are integrated using the concept of distribution, which involves using test functions to evaluate the integral.
Dirac Delta generalized functions have various applications in physics and engineering. For example, they are used to model point sources of gravitational and electromagnetic fields, and to describe the behavior of particles in quantum mechanics. They are also used in signal processing to represent impulse signals and in control systems to model instantaneous changes in a system.