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