Results 1 to 8 of 8

Math Help - laplace inverse

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    74

    laplace inverse

    Intergral from p to infinity of F(p)dp = laplace of f(t)/t
    I have to reverse the order of integration to show that those two are equivalent if F(p) = laplace of f(t)

    Not sure how to do this, If i reverse the order of integration is it the integral from 0 to t?

    Do i use the convolution theorem where g(u) = 1?

    these are the ideas I have but not sure if it is right now not
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by CookieC View Post
    Intergral from p to infinity of F(p)dp = laplace of f(t)/t
    I have to reverse the order of integration to show that those two are equivalent if F(p) = laplace of f(t)

    Not sure how to do this, If i reverse the order of integration is it the integral from 0 to t?

    Do i use the convolution theorem where g(u) = 1?

    these are the ideas I have but not sure if it is right now not
    Are you trying to prove that if LT[f(t)] = F(p) then \displaystyle LT\left[\frac{f(t)}{t}\right] = \int_p^{+\infty} F(u) \, du ? Please post the question exactly as it is written.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2010
    Posts
    74
    yeah that's what i'm trying to prove sorry about the badly typed question
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mr fantastic View Post
    Are you trying to prove that if LT[f(t)] = F(p) then \displaystyle LT\left[\frac{f(t)}{t}\right] = \int_p^{+\infty} F(u) \, du ? Please post the question exactly as it is written.
    \displaystyle LT\left[ \frac{f(t)}{t} \right] = \int_0^{+\infty} f(t) \frac{1}{t} e^{-pt} \, dt = \int_0^{+\infty} f(t) \left[ \int_{p}^{+\infty} e^{-ut} \, du \right] \, dt


    \displaystyle = \int_p^{+\infty} \left[ \int_{0}^{+\infty} f(t) e^{-ut} \, dt \right] \, du = \int_p^{+\infty} F(u) \, du .
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    May 2010
    Posts
    74
    Where did the 1/t go after the second equals sign?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by CookieC View Post
    Where did the 1/t go after the second equals sign?
    Perhaps your question should be "Where did that second integral come from that's inside the first integral?". It could be that the two questions are related ....
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    May 2010
    Posts
    74
    I thought the second integral just came from the definition of the laplace transform....
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by CookieC View Post
    I thought the second integral just came from the definition of the laplace transform....
    You really need to think harder about the help you get given. I thought it would be obvious that I was referring to the second integral that is inside of

    \displaystyle \int_0^{+\infty} f(t) \left[ \int_{p}^{+\infty} e^{-ut} \, du \right] \, dt.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Laplace/Inverse Laplace Questions
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 14th 2010, 11:29 AM
  2. Help with inverse laplace
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: July 15th 2010, 03:11 PM
  3. Inverse Laplace
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 16th 2009, 02:22 AM
  4. Inverse Laplace
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: June 1st 2009, 08:54 PM
  5. Inverse Laplace
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 1st 2008, 03:41 AM

Search Tags


/mathhelpforum @mathhelpforum