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We can define the Fourier sine transform as $$F[f(x)](s)=\int_{-\infty}^{+\infty}f(x) \sin (sx) dx\:.$$

Now the inverse sine transform is $$f(x) =\int_{-\infty}^{+\infty}F(s) \sin (sx) ds\:.$$

I have used this formula to evaluate the value of $f(x)$ but I can't.

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  • $\begingroup$ please use latex commands to produce a better layout for the question $\endgroup$ Apr 29 '21 at 19:21
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    $\begingroup$ Is this about Mathematics? $\endgroup$
    – JAlex
    Apr 29 '21 at 19:33
  • $\begingroup$ What is your function? $F(s) = 2\pi\sqrt s$? Shouldn't it be an odd function (and defined everywhere)? $\endgroup$
    – doetoe
    Apr 29 '21 at 20:44
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    $\begingroup$ But indeed, better ask to have this question moved to mathematics. $\endgroup$
    – doetoe
    Apr 29 '21 at 20:46
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The problem that you ask has no answer because $\sqrt{s}$ is imaginary for for negtaive $s$. The answer that I think you are after is problem 1) part (b) of this homework set. I think that there is enough explained there for you to finish it off yourself.

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