Laplace transform of te^t

  • Thread starter Pi Face
  • Start date
  • #1
Pi Face
76
0

Homework Statement



f(t)=te^t, find laplace

Homework Equations





The Attempt at a Solution



I started doing integration by parts and after doing it three times I wasn't sure if I was going in the right direction/making any progress. I'm not supposed to use a table to solve this (I have to do the integral out) so could anyone give me a hint as to how to start?

I can manipulate the original equation to
(0 to inf for all integrals)
∫ te^(t(1-s)) dt and then i set u=t, du=dt, dv=e^(t(1-s)), v=e^(t(1-s))/(1-s)
and then I end up with a longer expression and I need to integrate by parts again. is this is right direction?
 

Answers and Replies

  • #2
susskind_leon
179
0
It's the right direction. After all, your t-factor in the integrand goes away, so you just have to integrate e^(t*something).
 
  • #3
Pi Face
76
0
I think I'm missing a step.

after doing interation by parts the first time, i get

te^[t(1-s)] / (1-s) - ∫ e^[t(1-s)] / (1-s) dt

=te^[t(1-s)] / (1-s) - e^[t(1-s)] / (1-s)^2

i then need to evaluate fro 1 to inf but what does that do to te^[t(1-s)], assuming s>1? t is inf and e^[t(1-s)] becomes 0?

EDIT: nevermind, I had a brainfart, I got the answer
 
Last edited:
  • #4
sunjin09
312
0
I think I'm missing a step.

after doing interation by parts the first time, i get

te^[t(1-s)] / (1-s) - ∫ e^[t(1-s)] / (1-s) dt

=te^[t(1-s)] / (1-s) - e^[t(1-s)] / (1-s)^2

i then need to evaluate fro 1 to inf but what does that do to te^[t(1-s)], assuming s>1? t is inf and e^[t(1-s)] becomes 0?

Laplace transform generally has a region of convergence to the right of some axis parallel to the y-axis on the complex s plane, in this case this axis happens to be x=1.
 

Suggested for: Laplace transform of te^t

  • Last Post
Replies
6
Views
428
  • Last Post
Replies
3
Views
300
  • Last Post
Replies
10
Views
624
  • Last Post
Replies
4
Views
514
Replies
3
Views
362
Replies
5
Views
342
Replies
2
Views
277
Replies
9
Views
377
Replies
0
Views
194
Replies
8
Views
670
Top