Inverse Laplace transform of 1/s

Step by step, with the reason for every step · The inverse Laplace transform · Differential Equations

Step by step

Question: find the inverse Laplace transform of 1 over s.

ℒ⁻¹{1s} =

The inverse transform goes back: which function of t has this transform?

We read the table backwards.

ℒ⁻¹: back from s to t

Each piece is already a row of the table.

1 → 1s

Read the table backwards, piece by piece: 1.

f(t) = 1

Let's check: the table forwards turns our answer back into 1 over s.

Right!

forwards: 1 → 1s

Let's look back.

First: use the table backwards.

Last: check.

Answer

f(t) = 1

Try this one yourself, then check:

ℒ⁻¹{1s − 1}

Show the answer

f(t) = e^(t)