Re: Table to find lower and upper estimate
- To: mathgroup at smc.vnet.net
- Subject: [mg68219] Re: Table to find lower and upper estimate
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Sat, 29 Jul 2006 01:00:53 -0400 (EDT)
- Organization: The University of Western Australia
- References: <ea72lp$k6p$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <ea72lp$k6p$1 at smc.vnet.net>,
"T Harris" <tdh1967 at bellsouth.net> wrote:
> 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.
Another approach to solving this problem is interpolation.
> A table of values of an increasing function f is shown. Use the table to
> find lower and upper estimates for f(x) dx.
xdata = {0, 5, 10, 15, 20, 25};
fdata = {-42, -37, -25, -6, 15, 36};
Lower estimate:
lower = Interpolation[Transpose[{xdata, RotateRight[fdata]}],
InterpolationOrder -> 0]
Plot[lower[t], {t, 0, 25}]
Integrate[lower[t], {t, 0, 25}]
-475
Upper estimate:
upper = Interpolation[Transpose[{xdata, fdata}],
InterpolationOrder -> 0]
Plot[upper[t], {t, 0, 25}]
Integrate[upper[t], {t, 0, 25}]
-85
Cubic interpolation:
int = Interpolation[Transpose[{xdata, fdata}]]
Plot[int[t], {t, 0, 25}]
Integrate[int[t], {t, 0, 25}]
-6905/24
with numerical value
N[%]
-287.7083333333333
Cheers,
Paul
_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
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