Calculating the Fourier Transform of f(x) = 1 if -1<x<1, f(x) = 0 otherwise

[leopard]

Homework Statement

Find the Fourier transform of the function f(x) = 1 if -1<x<1, f(x) = 0 otherwise

2. The attempt at a solution

\hat{f}(w) = \frac{1}{\sqrt{2 \pi}} \int ^{1}_{-1}e^{-iwx}dx = \frac{1}{\sqrt{2 \pi}} [\frac{e^{-iwx}}{-iw}]^{1}_{-1} = \frac{1}{-iw \sqrt{2 \pi}}(e^{-iw} - e{iw}) = \sqrt{\frac{2}{\pi}} \frac{sinw}{w}

According to my book, the correct answer is \sqrt{\frac{\pi}{2}} \frac{sinw}{w}

Who is right?

 

[weejee]

I can't find any mistakes in your solution.