Hi All,
Given the following data below:- (data points at increments of {1,2,3,4,5,6,7,8,9,10...etc } I have plotted the data as blue points. (Almost linear, but not...) I have also plotted to g = Interpolation[data] as a line through the data... My question - I am trying to calculate the definite Integral to represent the Volume of a right squared pyramid from height 15 to 60 for example . The x axis being the height of the pyramid & the slope plotted being half of the cross section of the pyramid along 1/2 side of the square base. I have setup a bestFitLine function to give approx value guidance. But I really want to get the pyramid volume from the actual (uneven) data points / interpolation.
In[1]:= data = {1.2010674083676476`, 1.4610596766655415`,
1.6961372700361923`, 1.9184860674104527`, 2.132494637438493`,
2.3403777349216415`, 2.5434607491172385`, 2.7426285002921538`,
2.9385199513793783`, 3.1316244697300593`, 3.322334014583465`,
3.5109733543607615`, 3.6978183572141328`, 3.883107474330874`,
4.067049224023154`, 4.249827238220414`, 4.431603766561531`,
4.6125221801690985`, 4.792708823563339`, 4.972274451728503`,
5.151315417828051`, 5.329914725543849`, 5.508143020159319`,
5.686059561839028`, 5.863713201765801`, 6.041143366150418`,
6.2183810432789945`, 6.395449763257905`, 6.57236655769515`,
6.749142886197359`, 6.925785517542216`, 7.1022973552487505`,
7.278678199637739`, 7.454925441030723`, 7.631034681224503`,
7.807000282628627`, 7.982815846373875`, 8.158474622252527`,
8.333969854531446`, 8.509295068502324`, 8.684444303131702`,
8.85941229539189`, 9.03419462184462`, 9.208787802865604`,
9.383189374589788`, 9.557397933267952`, 9.731413156292543`,
9.90523580370352`, 10.078867703545864`, 10.25231172403398`,
10.425571735093747`, 10.598652561505094`, 10.771559929557819`,
10.94430040885976`, 11.116881350696419`, 11.289310824131494`,
11.46159755085488`, 11.633750839625161`, 11.805780521014597`,
11.977696883043432`, 12.149510608185144`, 12.321232712132687`,
12.492874484636884`, 12.664447432659893`, 12.835963226028221`,
13.007433645719672`, 13.17887053487611`, 13.350285752597737`,
13.521691130544323`, 13.693098432343339`, 13.864519315783989`,
14.035965297758807`, 14.207447721900595`, 14.37897772885137`,
14.550566229091388`, 14.722223878249748`, 14.893961054813387`,
15.065787840147776`, 15.237714000740603`, 15.409748972578276`,
15.581901847564591`, 15.75418136189079`, 15.926595886266563`,
16.0991534179222`, 16.271861574292842`, 16.444727588296836`,
16.61775830512115`, 16.79096018042811`, 16.96433927989891`,
17.137901280030547`, 17.311651470104557`, 17.48559475524697`,
17.659735660500854`, 17.834078335834207`, 18.008626562007777`,
18.183383757229233`, 18.35835298452189`, 18.533536959738324`,
18.708938060151258`, 18.884558333556175`, 19.060399507822524`,
19.236463000832632`, 19.4127499307499`, 19.589261126560302`,
19.76599713883387`, 19.94295825065534`, 20.120144488675827`,
20.29755563424022`, 20.4751912345474`, 20.653050613803487`,
20.831132884330703`, 21.00943695759741`, 21.18796155513734`,
21.36670521932895`, 21.545666324008142`, 21.724843084890374`,
21.904233569780544`, 22.083835708551472`, 22.263647302874112`,
22.443666035684856`, 22.623889480377454`, 22.804315109709016`,
22.984940304411634`, 23.16576236150283`, 23.346778502289833`,
23.527985880064236`, 23.70938158748511`, 23.890962663649997`,
24.072726100854435`, 24.2546688510419`, 24.436787831947047`,
24.619079932936078`, 24.80154202054889`, 24.98417094374854`,
25.166963538884048`, 25.349916634373205`, 25.53302705511266`,
25.716291626622777`};
g = Interpolation[data]
bestFitLine[x_] := 1.413481098702441` + 0.1753779788405405` x
See attached file = "Question - Integrate from InterpolatingFunction - 3rd Octo 2018.nb" for plotted lines & data. And required result.
Please could anyone show me the correct coding for an interpolating function from the data to give accurate volume of pyramid at any point along the x / height domain.
Many thanks for your help & attention. Best regards, Lea...
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