What is the integral from-infinity to infinity of e^{-jwt} ?

The integral from-infinity to infinity of e^{-jwt} is diverges

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integral from-infinity to infinity of e^{-jwt}

\int_{- \infty}^{\infty} e^{- j wt} d t

diverges

Solution steps

\int_{- \infty}^{\infty} e^{- j wt} d t

Compute the indefinite integral:

\int e^{- j wt} d t = - \frac{1}{w j} e^{- w j t} + C

Compute the boundaries:

\int_{- \infty}^{\infty} e^{- j wt} d t =

diverges

= diverges

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What is the integral from-infinity to infinity of e^{-jwt} ?
The integral from-infinity to infinity of e^{-jwt} is diverges