Results 1 to 10 of 10
Like Tree1Thanks
  • 1 Post By romsek

Math Help - Power series integrastion

  1. #1
    Newbie
    Joined
    Jun 2014
    From
    Kongsberg
    Posts
    23

    Power series integrastion

    How i can integrate this by using powe series


    int from 0 to 2x ((e^t)-1)/(t)) dt


    thanx
    Last edited by Haytham1111; July 13th 2014 at 10:39 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,448
    Thanks
    940

    Re: Power series integrastion

    is this $e^t-1$ or $e^{t-1}$ ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2014
    From
    Kongsberg
    Posts
    23

    Re: Power series integrastion

    The first one (e^t)-1
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,448
    Thanks
    940

    Re: Power series integrastion

    Quote Originally Posted by Haytham1111 View Post
    The first one (e^t)-1
    so you want

    $\displaystyle{\int_0^{2x}}\dfrac{e^t-1}{t}~dt$

    First thing you do is express the integrand in terms of a power series.

    $e^t-1=\displaystyle{\sum_{k=1}^\infty}\dfrac {t^k}{k!}$

    so

    $\dfrac {e^t-1}{t} = \displaystyle{\sum_{k=1}^\infty}\dfrac {t^{k-1}}{k!}$

    now just integrate that term for term. I leave this to you.
    Thanks from Haytham1111
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2014
    From
    Kongsberg
    Posts
    23

    Re: Power series integrastion

    The express u did is just for (e^t) and not for (e^t)-1 . I got the wrong answer
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,448
    Thanks
    940

    Re: Power series integrastion

    Quote Originally Posted by Haytham1111 View Post
    The express u did is just for (e^t) and not for (e^t)-1 . I got the wrong answer
    did you note that the series starts at $k=1$ and not $k=0$ ?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jun 2014
    From
    Kongsberg
    Posts
    23

    Re: Power series integrastion

    What is that mean?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Jun 2014
    From
    Kongsberg
    Posts
    23

    Re: Power series integrastion

    When u have e^t -1. Is not mean that u need to trekk 1 from each ledd in the series?

    So it will be ((x^n)/n!) - 1 = ((x^n-n!))/n!. I understand it like that


    And when u make reindeksing, Then thats mean that u put n-1 in the serie for each n, Then you will start from n=1 and not n=0
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Jun 2014
    From
    Kongsberg
    Posts
    23

    Re: Power series integrastion

    Ja ja. I understood it noe. You remove just one from Hole series, and not from each ledd. Then u r right, and i got the right answer. Tanx very much
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Jun 2014
    From
    Kongsberg
    Posts
    23

    Re: Power series integrastion

    Can u tell me how u can write the series index? I use the ipad, do u know an another way to write it?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 18th 2013, 07:27 PM
  2. Replies: 2
    Last Post: December 9th 2012, 12:50 PM
  3. Replies: 3
    Last Post: September 29th 2010, 06:11 AM
  4. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  5. Replies: 10
    Last Post: April 18th 2008, 10:35 PM

Search Tags


/mathhelpforum @mathhelpforum