Math Problem Solver

Use Definition 7.1.1.

DEFINITION 7.1.1 Laplace Transform

Let f be a function defined for

t ≥ 0.

Then the integral

ℒ{f(t)} =

∞

e−stf(t) dt

0

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

Find

ℒ{f(t)}.

(Write your answer as a function of s.)

f(t) =

−1, 0 ≤ t < 1

1, t ≥ 1

ℒ{f(t)} =