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!

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


    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: How to prove the formula for L{tf(t)}?
  1. Proving a formula (Replies: 4)