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Re: Table to find lower and upper estimate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68179] Re: Table to find lower and upper estimate
  • From: "Norbert Marxer" <marxer at mec.li>
  • Date: Thu, 27 Jul 2006 05:30:04 -0400 (EDT)
  • References: <ea72lp$k6p$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hello

If you use the following functions ...

 - Drop[...] to drop the first or last element of the list
 - Dot[...] or "." (i.e. scalar product) to build the sum of the areas

... you will get the lower und upper bounds for your integral with the
following commands:

    xList = {0, 5, 10, 15, 20, 25};
    fList = {-42, -37, -25, -6, 15, 36};
    dxList = Drop[xList, 1] - Drop[xList, -1]
    lowerBound = Drop[fList, 1].dxList
    upperBound = Drop[fList, -1].dxList

Because your intervals (dx) are equidistant you could also use: dxList
= Table[5,{5}]

Note that if your function is not increasing (or decreasing) you would
have to find the maximum or minimum in each interval.

Best Regards
Norbert Marxder
www.mec.li


T Harris wrote:
> Hello,
>
>
>
> I hope someone could tell me where to look to or if easy enough, to advise
> me on how to use Mathemetica for the type of problem I have below.  I
> already have worked it and have the lower estimate to be -475 and the upper
> estimate to be -85.  I was hoping to put Mathematica to a practical use here
> and I really don't know how to do this.   I have typed the problem in
> exactly as shown in James Stewart's, Calculus 5th Edition.
>
>
>
> Here it is:
>
> A table of values of an increasing function f is shown.  Use the table to
> find lower and upper estimates for  f(x) dx.
>
>       x
>      0
>      5
>      10
>      15
>      20
>      25
>
>       f(x)
>      -42
>      -37
>      -25
>      -6
>      15
>      36
> 
> 
> 
> 
> Thanks to anyone with advice.
> 
> 
> T Harris


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