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