# How do you find $f(x)$ if its sine transform is $2πs^{½}$?

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.

• please use latex commands to produce a better layout for the question Apr 29 '21 at 19:21
• Is this about Mathematics? Apr 29 '21 at 19:33
• What is your function? $F(s) = 2\pi\sqrt s$? Shouldn't it be an odd function (and defined everywhere)? Apr 29 '21 at 20:44
• But indeed, better ask to have this question moved to mathematics. Apr 29 '21 at 20:46

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.