Results 1 to 5 of 5

Math Help - Laplace transform help

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    48

    Laplace transform help

    Hey guys, I need some help with this problem:
    [tex]\int e^-^s^t cost dt lower limit is 0 and the upper limit is \infty [\math]

    The problem I am running into is when I use integration by parts. I let u = cost and dv = [tex] e^-^s^[\math]

    I am somehow getting stuck with an infinite integration by parts problem. Any help is greatly appreciated!!! Thank you!

    Sorry, for some reason the latex is not working the way I want it to.......
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Let

    I=\int_{0}^{\infty}e^{-st}\cos(t)\,dt.

    Let

    u=e^{-st},\quad du=-se^{-st}\,dt,\quad dv=\cos(t)\,dt,\quad v=\sin(t).

    We get

    I=e^{-st}\sin(t)\Big|_{0}^{\infty}+\int_{0}^{\infty}se^{-st}\sin(t)\,dt=s\int_{0}^{\infty}e^{-st}\sin(t)\,dt.

    Next, we let

    u=e^{-st},\quad du=-se^{-st}\,dt,\quad dv=\sin(t)\,dt,\quad v=-\cos(t).

    We get

    I=s\left[-e^{-st}\cos(t)\Big|_{0}^{\infty}-s\int_{0}^{\infty}e^{-st}\cos(t)\,dt\right]=s\left[1-sI\right].

    It is that last step there, recognizing that we've arrived back at I, that is the crucial one. You now have an equation for I. Solve for it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2
    I think we're back to [TEX ] ... [/TE X]
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Jeonsah View Post
    Hey guys, I need some help with this problem:
    [tex]\int e^-^s^t cost dt lower limit is 0 and the upper limit is \infty [\math]

    The problem I am running into is when I use integration by parts. I let u = cost and dv = [tex] e^-^s^[\math]

    I am somehow getting stuck with an infinite integration by parts problem. Any help is greatly appreciated!!! Thank you!

    Sorry, for some reason the latex is not working the way I want it to.......
    Don't use integration by parts! Either use the complex exponential form for \cos (t):

     \cos(t) = \frac{e^{it}+e^{-it}}{2}

    or write your integral as:

    \int_0^{\infty}e^{-st}\cos(t)\; dt= \text{re}\left(\int_0^{\infty}e^{-st}e^{it}\; dt \right)

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Oct 2009
    Posts
    48
    Thanks guys, i figured it out with integration by parts. Ima make another topic with a couple new questions with the laplace transform.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Laplace transform of |sin(t)| ?
    Posted in the Calculus Forum
    Replies: 23
    Last Post: January 3rd 2011, 03:14 PM
  2. Laplace transform and Fourier transform what is the different?
    Posted in the Advanced Applied Math Forum
    Replies: 8
    Last Post: December 29th 2010, 10:51 PM
  3. Laplace Transform (3)
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: August 15th 2010, 12:41 AM
  4. Laplace Transform
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 8th 2009, 04:54 AM
  5. Laplace Transform
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 10th 2008, 10:46 PM

Search Tags


/mathhelpforum @mathhelpforum