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Re: Table to find lower and upper estimate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68164] Re: Table to find lower and upper estimate
  • From: Peter Pein <petsie at dordos.net>
  • Date: Thu, 27 Jul 2006 05:29:43 -0400 (EDT)
  • References: <ea72lp$k6p$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

T Harris schrieb:
> 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,

  you're absolutely right:

In[1]:=
data = Transpose[{5*Range[0, 5], {-42, -37, -25, -6, 15, 36}}]
Out[1]=
{{0, -42}, {5, -37}, {10, -25}, {15, -6}, {20, 15}, {25, 36}}
In[2]:=
lowsum = Total[((#1[[2,1]] - #1[[1,1]])*#1[[1,2]] & ) /@ Partition[data, 2, 1]]
Out[2]=
-475
In[3]:=
highsum = Total[((#1[[2,1]] - #1[[1,1]])*#1[[2,2]] & ) /@ Partition[data, 2, 1]]
Out[3]=
-85

Peter


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