first shifting
Problem 03 | Evaluation of Integrals
Problem 03
Find the value of $\displaystyle \int_0^\infty te^{-3t} \sin t ~ dt$
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Problem 04 | First Shifting Property of Laplace Transform
Problem 04
Find the Laplace transform of $f(t) = e^t \sinh 2t$.
Problem 03 | First Shifting Property of Laplace Transform
Problem 03
Find the Laplace transform of $f(t) = e^{-3t} \cos t$.
Problem 02 | First Shifting Property of Laplace Transform
Problem 02
Find the Laplace transform of $f(t) = e^{-5t} \sin 3t$.
Problem 01 | First Shifting Property of Laplace Transform
Problem 01
Find the Laplace transform of $f(t) = e^{2t}t^3$.
First Shifting Property | Laplace Transform
First Shifting Property
If $\mathcal{L} \left\{ f(t) \right\} = F(s)$, when $s > a$ then,
$\mathcal{L} \left\{ e^{at} \, f(t) \right\} = F(s - a)$
In words, the substitution $s - a$ for $s$ in the transform corresponds to the multiplication of the original function by $e^{at}$.
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