I am trying to solve:
Calculate Fourier transform (on $-\infty < x < \infty $) of:
$$ f(x) = \begin{cases} 1, & -L<x<L \\ 0, & |x|\geq L \end{cases} $$
My Solution: $$ \hat f(k) = \int_{-L}^{L} e^{-ikx}dx = -\frac{e^{-ikx}}{ik}|_{-L}^{L} = \frac{e^{ikl}-e^{-ikl}}{ik} = \frac{2sinkl}{k}$$
What do you think, am I right? Thanks!