1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: How to prove the formula for L{tf(t)}?

  1. Jan 6, 2012 #1
    1. The problem statement, all variables and given/known data
    L{tf(t)} denotes the Laplace transform of tf(t). I know that it's equal to -dF(s)/ds (where F(s)=L{f(t)}) from a Laplace transform table but I don't know how to prove that.
     
  2. jcsd
  3. Jan 6, 2012 #2
    What is the definition of L{tf(t)}??
     
  4. Jan 6, 2012 #3
    [tex] \int^\infty_{0} tf(t)e^{-st} dt[/tex]

    I've tried integration by parts, but it didn't help.
     
  5. Jan 6, 2012 #4
    OK, so I think it's best to start with

    [tex]F(s)=\int_0^\infty{f(t)e^{-ts}dt}[/tex]

    Now we wish to find [itex]F^\prime (s)[/itex]. Do you know Leibniz integral rule??
     
  6. Jan 6, 2012 #5
    No. state the rule please.
     
  7. Jan 6, 2012 #6
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...