Results 1 to 12 of 12
Like Tree1Thanks
  • 1 Post By romsek

Thread: Integration

  1. #1
    Newbie
    Joined
    Aug 2015
    From
    Malaysia
    Posts
    9

    Integration

    Please am stuck with the integration I kindly need assistance in solving this equation, I will really appreciate if anyone could help with the solution or a guide on what i should do

    \int\limits_0^\infty  {\log (1 + \frac{a}{b}x)\frac{{N{e^{ - x}}{x^{y - 1}}}}{{\left( {y - 1} \right)!}}} {\left( {1 - {e^{ - x}}\sum\limits_{i = 0}^{y - 1} {\frac{{{x^i}}}{{i!}}} } \right)^{N - 1}}dx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,473
    Thanks
    1688

    Re: Integration

    Hey Igbafe.

    Are the y and x variables independent or not?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2015
    From
    Malaysia
    Posts
    9

    Re: Integration

    a,b,y and N are sets of constants
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,418
    Thanks
    2291

    Re: Integration

    Mathematica chewed on it for a bit and could not come up with an answer.

    Please post your question only once.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,473
    Thanks
    1688

    Re: Integration

    Are you looking for an estimate or an analytic expression?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Aug 2015
    From
    Malaysia
    Posts
    9

    Re: Integration

    An analytical expression
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Matt Westwood's Avatar
    Joined
    Jul 2008
    From
    Reading, UK
    Posts
    1,281
    Thanks
    197

    Re: Integration

    What is the context? Is it an exercise from an insanely difficult course on analysis, or does it arise during the course of real-world research?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Aug 2015
    From
    Malaysia
    Posts
    9

    Re: Integration

    it arise during the course of real-world research from a MIMO communication point of view where the best set of Nt out of Nr antennas are selected for transmission and received by Nd antennas. N=combination of(Nr,Nt) while y=(Nt*Nd) hence N and y will be constants depending on wat values of antenna that are available hence am trying to have an analytical expression in terms of N and y
    Last edited by Igbafe; Aug 9th 2015 at 04:46 PM.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor Matt Westwood's Avatar
    Joined
    Jul 2008
    From
    Reading, UK
    Posts
    1,281
    Thanks
    197

    Re: Integration

    My initial suggestion is that you are going to need to either:
    a) simplify your expression
    b) simplify your model
    c) use linear approximations for the exponentials and logarithm in the integral
    d) use numerical methods.

    My gut instinct would be to go for d) and write a computer program to do the heavy lifting -- but it would be a project that I expect would take me a number of weeks, months even.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Aug 2015
    From
    Malaysia
    Posts
    9

    Re: Integration

    updates on some work already done. Basically the equation if of the form


    C(N) = \int\limits_0^\infty  {{I_{(N)}}{p_{(N)}}} dx


    where

    {I_{(N)}} = \log \left( {1 + \frac{a}{b}x} \right)

    and

    {p_{(N)}}(x) = \frac{{N\left( {{e^{ - x}}{x^{y - 1}}} \right)}}{{\left( {y - 1} \right)!}}{\left( {1 - {e^{ - x}}\sum\limits_{i = 0}^{y - 1} {\frac{{{x^i}}}{{i!}}} } \right)^{N - 1}}

    we have been able to integrate
    {p_{(N)}}
    within the limits of [0,t] as


    \int_0^t {{p_{(N)}}} (x)dx = \int_0^t {\frac{{N\left( {{e^{ - x}}{x^{y - 1}}} \right)}}{{\left( {y - 1} \right)!}}} {\left( {1 - {e^{ - x}}\sum\limits_{i = 0}^{y - 1} {\frac{{{x^i}}}{{i!}}} } \right)^{N - 1}}dx = \frac{N}{{\left( {y - 1} \right)!}}\sum\limits_{i = 0}^{N - 1} {{{\left( { - 1} \right)}^i}} \left( \begin{array}{c} N - 1\\ i \end{array} \right)\sum\limits_{h = 0}^{i(y - 1)} l \left( {y,\:i} \right)\left[ { - {e^{ - \left( {i + 1} \right)t}}\sum\limits_j^{y + h - 1} {\frac{{j!\left( \begin{array}{c} y + h - 1\\ j \end{array} \right)}}{{{{\left( {i + 1} \right)}^{j + 1}}}}} {t^{y + h - j - 1}} + \frac{{\left( {y + h - 1} \right)!}}{{{{\left( {i + 1} \right)}^{y + h}}}}} \right]



    I don't know if this could help in anyway in solving my problem above
    Last edited by Igbafe; Aug 9th 2015 at 09:46 PM.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,473
    Thanks
    1688

    Re: Integration

    Can you get a Taylor series like expansion and cut it off for some error boundary term and integrate the partial series?
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Aug 2015
    From
    Malaysia
    Posts
    9

    Re: Integration

    okay i will appreciate any help on that
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Nov 3rd 2010, 12:54 AM
  2. Replies: 2
    Last Post: Nov 2nd 2010, 04:57 AM
  3. Replies: 8
    Last Post: Sep 2nd 2010, 12:27 PM
  4. Replies: 2
    Last Post: Feb 19th 2010, 10:55 AM
  5. Replies: 6
    Last Post: May 25th 2009, 06:58 AM

Search Tags


/mathhelpforum @mathhelpforum