Integral using parseval (supposed to be simple )

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In summary, the conversation is about a person who is struggling with a seemingly simple integral problem and is looking for someone to explain the steps. The conversation also mentions the use of Parseval, but it is unclear how it relates to the problem.
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jjongmu
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integral using parseval (supposed to be simple :( )

Hi everyone. I am stuck in one of the assignment problems, and I think it's supposed to be simple, but it's just that I don't see how it worked out.

I have to take integral(1/a^2+w^2)dw, from -a to a.
I know the answer but I have no single clue how it came out.
It would be great if someone could explain with steps :(
Thank you and have a great day.
 
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  • #2


Do you mean this?
[tex]\int \frac{1}{a^2+w^2}dw = \frac{1}{a}\tan^{-1}\frac{w}{a}+c[/tex]

or this?

[tex]\int \left(\frac{1}{a^2}+{w^2}\right)dw = \ldots [/tex]

Why Parseval?
 

What is Parseval's theorem?

Parseval's theorem is a mathematical theorem that relates the integral of the squared magnitude of a function to the integral of the squared magnitude of its Fourier transform. It is also known as the energy conservation theorem.

How is Parseval's theorem used in integrals?

Parseval's theorem can be used to simplify integrals by allowing them to be calculated in the frequency domain instead of the time domain. This can make certain integrals easier to solve and can also help with convergence issues.

What is the significance of using Parseval's theorem in integrals?

Using Parseval's theorem in integrals can help to simplify complex integrals and can also provide a way to check the accuracy of numerical integration methods. It also has applications in signal processing and engineering.

Can Parseval's theorem be used for both continuous and discrete functions?

Yes, Parseval's theorem can be used for both continuous and discrete functions. However, different versions of the theorem exist for each case.

How does Parseval's theorem relate to the concept of energy?

Parseval's theorem relates to the concept of energy by stating that the total energy of a signal is conserved in both the time and frequency domains. This means that the energy of a signal can be calculated using either the integral of the squared magnitude of the signal or the integral of the squared magnitude of its Fourier transform.

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