Question

Is there a mistake in the FT identity of integration, if yes what is the right one​

Answer 1

The right one is;

`{ \rm{ (1)/( \omega) x(t) \to \int X( \omega)}}`

X(w) is the fourier transform and the FT pair identity is as below;

`{ \tt{x(t) =X( \omega) {e}^{ - (k \omega _(0)t )} \: dt }} \\ { \tt{x(t) = \int X( \omega) { e}^{ - (k\omega _(0)t)} d t}} \\ { \tt{x(t) = k\omega _(0) \{x( \omega) {e}^{ -k(\omega _(0)t) } }}`

Assume k is 1

`{ \tt{ (x(t))/(\omega _(0)) = \int x( \omega _(0)) }}`