Help getting started with this integral

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In summary, The conversation is about a person having trouble understanding how to evaluate a particular integral and is seeking help. They are trying to express a polar wave as a summation of plane waves and the integral in question appears when solving for the amplitudes of the plane waves. The other person suggests checking if the integral is convergent and questions its physical meaning. The original person also asks for a reference or techniques to help with the integral.
  • #1
CuppoJava
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Hello everyone,

I'm having trouble understanding how to evaluate this integral. I am not sure whether there is a closed form solution.

[itex]\int_{-\infty}^\infty e^{-j\sqrt{x^2+a^2}} e^{-jkx} dx[/itex]

I am trying to express a polar wave as a summation of plane waves, and this integral drops out when solving for the amplitudes of the plane waves. Thanks very much for your help. A link to a reference, or the necessary techniques would be very helpful.

-Patrick
 
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  • #2
Hi !

Did you first check if the integral is convergent or not ?
If not, are you sure that the given integral has a physical meaning ?
(I think that the integral is not convergent).
 
  • #3
A typo in your integral ?
 

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1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is a fundamental part of calculus and is used to solve a variety of problems in physics, engineering, and other fields.

2. How do I solve an integral?

To solve an integral, you can use various techniques such as substitution, integration by parts, and trigonometric identities. It is important to first identify the type of integral you are dealing with and then apply the appropriate method to solve it.

3. What is the purpose of solving integrals?

Solving integrals helps us to find the exact value of the area under a curve, which can be useful in calculating quantities like distance, velocity, and acceleration in physics. It also helps us to find the volume of irregular shapes, as well as to solve optimization problems in economics and engineering.

4. Can integrals be solved by hand or do I need a computer?

Integrals can be solved by hand using various techniques, but for more complex integrals, a computer may be necessary. However, it is important to have a solid understanding of the concepts and techniques involved in order to use a computer effectively for solving integrals.

5. How can I improve my skills in solving integrals?

To improve your skills in solving integrals, it is important to practice regularly and to understand the underlying concepts. You can also seek help from textbooks, online resources, or a tutor. Additionally, it is helpful to work through a variety of problems with different levels of difficulty to challenge yourself and improve your problem-solving abilities.

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