Can the Fourier integral of sinw be solved with a misprint?

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The discussion centers on the Fourier integral of the function sin(w) and addresses a misprint in the expression involving the exponential term. The correct formulation should replace "ewEts" with "eiwEt" to ensure the integral converges properly. The integral in question is ∫e^(wE - iw)t from -∞ to ∞, and the divergence issue arises from the real part wE if not handled correctly. Clarification on these points is essential for accurate computation of the Fourier integral.

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I'm a little unsure of how the attached solutions are obtained. For instance one of the Fourier integrals is:

∫e(wE-iw)t = [1/(wE-iw)e(wE-iw)t from -∞ to ∞. But what do you do about the real part wE? That leads the integral to diverge as far as I can see...
 

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hizezima1! :smile:

those ewEts are a misprint, they should be eiwEt :wink:
 

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