# Laplace transform help

1. Mar 22, 2012

### schapman22

1. The problem statement, all variables and given/known data
We have been given a table of laplace transforms and have been asked to show them using the definition. ∫0e-stf(t)dt.

But this one I have no clue where to begin
0tf(t)dt the laplace transform of this is F(s)/s.
Can anyone tell me what to do with this one? Thank you in advance.

2. Relevant equations

0e-stf(t)dt

0tf(t)dt transforms to F(s)/s

3. The attempt at a solution

I have it set up as
0[∫0tf(t)dt]e-stdt

2. Mar 22, 2012

### schapman22

Sorry I know it is difficult to read with the superscripts and subscripts. I didn't know a better way of displaying it.

3. Mar 22, 2012

### HallsofIvy

Staff Emeritus
Yes, that's correct. Now do the integral using integration by parts
Let "u" be $\int_0^t f(t)dt$. What is du?
Let "dv" be $e^{-st}dt$. What is v?

4. Mar 22, 2012

### QuarkCharmer

Check out the first part of the fundamental theorem of calculus, and think of that integral with the upper limit as t as some function.

5. Mar 22, 2012

### schapman22

Ok so du would be f(t)?
and v would be -1/s e-st

6. Mar 22, 2012

### QuarkCharmer

That's right!

7. Mar 23, 2012

### schapman22

Im sorry but im still having trouble with one. Can you help me with how to proceed?

8. Mar 23, 2012

### schapman22

I have it written out as uv - ∫vdu, but I dont know how to go from there.

9. Mar 23, 2012

### sunjin09

Try to prove the simpler but related problem using integration by parts, then you'll have some clue:
L{g'(t)}=sG(s)-g(0).
Then let g(t)=∫ _{0 to t} f(τ)dτ

10. Mar 23, 2012

### schapman22

thank you HallsofIvy, QuarkCharmer, and sunjin09.