Laplace transform of t

Step by step

The question

Question: find the Laplace transform of t.

1 The idea

The Laplace transform turns a function of t into a function of s.

It is an integral, but we almost never work it out: we use a table made from it.

The table rows we need.

2 Use the table

Each part by its row: t gives 1/s².

3 Check

Let's check: read the table backwards.

1/s² comes from t: the question.

Right!

Let's look back.

First: the idea.

Then: use the table.

Last: check.