Hi all

I know that the Fourier transform of x(t)=1 is X(jω)=2πδ(ω) by using the duality property.

This implies:

$\displaystyle \int_{-\infty }^{+\infty }e^{-j\omega t}dt=2\pi\delta(\omega)$

Consequently, for ω≠0:

$\displaystyle \int_{-\infty }^{+\infty }e^{-j\omega t}dt=0$

And as a result:

$\displaystyle \int_{-\infty }^{+\infty }\cos t\: dt=0$

Is this result true?!

Thanks in advance