Results 1 to 3 of 3

Math Help - Approximate integration

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    1

    Approximate integration

    Can anyone help me with what seems like an easy problem?

    Show that:

    (1/3)T_n + (2/3)M_n = S_2_n
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,977
    Thanks
    1121

    Re: Approximate integration

    Well, it would help if you told us what T_m, M_n, and S_ mean!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2010
    Posts
    92

    Re: Approximate integration

    I think he's using Simpson's rule. If I'm correct, it looks like he's trying to show the relation between the midpoint rule and the trapezoidal rule with Simpson's rule.

    Midpoint rule: M = (b-a)f(\frac{a+b}{s})

    Trapezoidal rule: T = \frac{1}{2}(b-a)(f(a)+f(b))

    Weighted average:

    \frac{2M+T}{3}

    This weighted average is Simpson's rule.

    Simpson's rule:

    \int_{a}^{b} f(x) dx \approx \frac{b-a}{6} \left[ f(a) + 4f\left(\frac{a+b}{2}\right)+f(b)\right]

    Looking at his equation,

    \frac{1}{3}T_{n} + \frac{2}{3}M_{n} = \frac{2M+T}{3} = weighted average = Simpson's Rule

    Not totally sure what these subscripts are, but there's a start.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. approximate log(1-x)
    Posted in the Calculus Forum
    Replies: 8
    Last Post: December 6th 2011, 08:09 AM
  2. Replies: 0
    Last Post: December 15th 2009, 08:05 AM
  3. Approximate Integration
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 4th 2009, 04:48 AM
  4. Approximate Integration - Trapezoidal Rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 22nd 2009, 04:26 AM
  5. Replies: 2
    Last Post: March 9th 2008, 12:09 PM

Search Tags


/mathhelpforum @mathhelpforum