What is laplacetransform t^3\delta(t-1) ?

The answer to laplacetransform t^3\delta(t-1) is e^{-s}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

laplacetransform t^3\delta(t-1)

laplace transform

t^{3} δ (t - 1)

e^{- s}

Solution steps

L {t^{3} δ (t - 1)}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

t^{3} δ (t - 1) : f (t) = δ (t - 1), k = 3

= (- 1)^{3} \frac{d ^{3}}{d s ^{3}} (L {δ (t - 1)})

L {δ (t - 1)} : e^{- s}

\frac{d ^{3}}{d s ^{3}} (e^{- s}) = - e^{- s}

= (- 1)^{3} (- e^{- s})

= e^{- s}

What is laplacetransform t^3\delta(t-1) ?
The answer to laplacetransform t^3\delta(t-1) is e^{-s}