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Re: Table to find lower and upper estimate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68188] Re: Table to find lower and upper estimate
  • From: "Valeri Astanoff" <astanoff at yahoo.fr>
  • Date: Sat, 29 Jul 2006 01:00:01 -0400 (EDT)
  • References: <ea72lp$k6p$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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

Hello T.

It seems convenient to use Interpolation
with InterpolationOrder set to 0
(a flat interpolation):

In[1]:=xi={0,5,10,15,20,25};
yi={-42,-37,-25,-6,15,36};

In[3]:=upperdata=Transpose[{xi,yi}]

Out[3]={{0,-42},{5,-37},{10,-25},{15,-6},{20,15},{25,36}}

In[4]:=upper=Interpolation[upperdata,InterpolationOrder -> 0];

In[5]:=Integrate[upper[x],{x,0,25}]

Out[5]=-85

In[6]:=loweryi=Prepend[Most[yi],0]

Out[6]={0,-42,-37,-25,-6,15}

In[7]:=lowerdata=Transpose[{xi,loweryi}]

Out[7]={{0,0},{5,-42},{10,-37},{15,-25},{20,-6},{25,15}}

In[8]:=lower=Interpolation[lowerdata,InterpolationOrder -> 0];

In[9]:=Integrate[lower[x],{x,0,25}]

Out[9]=-475
 

hth

Valeri


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