Let f(t) be a function on [0,00). The Laplace transform of f is the function F defined by the integral F(s) = e -stf(t) dt. Use this definition to determine the Laplace transform of the following function. f(t) = e - 6t + 5t3 – 81? The Laplace transform of f(t) is F(s) =||

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ISBN:9780470458365
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**Laplace Transform of a Function**

Let \( f(t) \) be a function on \([0, \infty)\). The Laplace transform of \( f \) is the function \( F \) defined by the integral:

\[
F(s) = \int_{0}^{\infty} e^{-st} f(t) \, dt
\]

Use this definition to determine the Laplace transform of the following function:

\[
f(t) = e^{-6t} + 5t^3 - 8t^2
\]

The Laplace transform of \( f(t) \) is \( F(s) = \, \Box \)
Transcribed Image Text:**Laplace Transform of a Function** Let \( f(t) \) be a function on \([0, \infty)\). The Laplace transform of \( f \) is the function \( F \) defined by the integral: \[ F(s) = \int_{0}^{\infty} e^{-st} f(t) \, dt \] Use this definition to determine the Laplace transform of the following function: \[ f(t) = e^{-6t} + 5t^3 - 8t^2 \] The Laplace transform of \( f(t) \) is \( F(s) = \, \Box \)
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