Considere f(x)=\left\{\begin{array}{lll}0 & \text { se } & x<0 \\\\ 1 & \text { se } & 0<x<2 \\\\ 0 & \text { se } & x>2\end{array}\right., encontre a transformada de Fourier de f dada pela fórmula
\mathcal{F}\{f\}(w)=\hat{f}(w)=\sqrt{\frac{1}{2 \pi}} \int_{-\infty}^{\infty} f(x) e^{-i w x} d x