Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform

Question

Question

Use Definition 7.1.1.

DEFINITION 7.1.1 Laplace Transform

Let $f$ be a function defined for $t \geq 0$. Then the integral

$$ \mathscr{L}\{f(t)\}=\int_{0}^{\infty} e^{-s t} f(t) d t $$

is said to be the Laplace transform of $f$, provided that the integral converges.

Find $\mathscr{L}\{f(t)\}$. (Write your answer as a function of s.)

$f(t)=\left\{\begin{array}{lr}t, & 0 \leq t<1 \\ 1, & t \geq 1\end{array}\right.$

Answer 1

Answer #1

Answer 2

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