Need help finding the fourier transform of xe^-x

[Megatron16]

Can anybody help in in finding the Fourier transform of f(x) = xe^-x where -1<x<0 and f(x)= 0 otherwise?

 

[SteamKing]

The range of x is missing a lower limit.

 

[Megatron16]

Oh sorry, the range of x is -1 < x < 0.

 

[SteamKing]

What's the definition of the Fourier transform of a function f(x)?

 

[Megatron16]

The formula is given in this link. I have to find G(w), and I have given f(t).
link: http://cnyack.homestead.com/files/afourtr/ftrt.gif

 

[Matterwave]

SteamKing is trying to get you to try to do this problem yourself. He knows the definition of a Fourier transform, but we want to see how you would approach this problem.