Indefinite Integrals / Laplace Transforms

1. May 15, 2007

EvanQ

1. The problem statement, all variables and given/known data

Using improper integrals, find the Laplace transform of f(t)=t, determining the values of s for which the transform is valid.

2. Relevant equations

The Laplace transform F(s) of a function f is defined as

/
F(s)= | f(t)e^(-st) dt.
/
0

3. The attempt at a solution

I have completely worked the question up until, and am pretty sure I know how to finish it off after integrating the Laplace transform function. It's been hinted at me to use integration by parts but I am completely lost at how to do this.

2. May 15, 2007

Dick

I'll give you a starting point. integral(t*exp(-s*t)*dt)=(-1/s)integral(t*d(exp(-s*t)). Now can you do the integration by parts on the parts t and exp(-s*t)?

3. May 15, 2007

Astronuc

Staff Emeritus
Generally for integration by parts -
$$\int_a^b f(x) g'(x)\,dx\,=\,\left[ f(x) g(x) \right]_{a}^{b} - \int_a^b f'(x) g(x)\,dx$$

let f(x) = t and g'(x) = e-st.

4. May 15, 2007

EvanQ

mmm thanks for the help guys, but it seems my problem was just a complete lack of knowledge on the topic, and even your help is going over my head.
looks like i'll just flunk this question and hit the books so it doesn't happen again.

5. May 15, 2007

Dick

Hitting the books as a response to flunking a question shows wise judgement. Good luck. Tackling Laplace transforms w/o a knowledge of integration by parts is probably a poor idea. Just to tease, can you do the Laplace transform of 1? Differentiate it with respect to s.