Sinusoidal regime and Fourier 1 Attachment(s) Am  amplitude; ψ  (starting) phase; Please, check out these equations... Tell me, please, are they correct or not? I need a simple YES/NO answer. I have not sufficient knowledge to understand them. I just need to know whether they are correct.... Thank you!!! P.S. It is a form of Fourier's inverse transform applied in electromagnetism... 
I found the attachment hard to read like it has transparent fonts or something. Do you understand the principles of a fourier transform and how to check your results? Crudely speaking its a plot of the amplitudes against the frequency of a fourier series (ignoring complex and imaginary terms). The inverse transform is going back the other way and basically recovering the wave form from a list of amplitude/frequency pairs. If you convert the integral into a Riemann sum you could approximate it. It's best not to try to work with this stuff blind but understand the principles behind it and then you can check your results (or be able to roughly guess or approximate what the answer should look like). I am sure I could dig up some youtube video lectures on fourier analysis, something like: PS: That's the problem with a calculator/computer society is that an over dependence on them takes away our ability to think for ourselves. 
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OK, did that and yes it is clearer. To attempt to answer your question, no, it doesn't look like a generalised inverse fourier transform. For instance they move the amplitude A as though it were a constant factor outside of the integral. Usually amplitude depends on frequency so this looks like something different. It might possibly be just a fourier series with a phase shift but not entirely sure what the maths is about here. 
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