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