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Numerical integration from uploaded file
  Numerically integrates given data at equally spaced abscissas.
2024.Jul.03 18:26:34
File to upload (with odd number of points, m, if Simpson)
Δx Interval width (iff 0, get it from X data). •
kol Y data column № in file. •
Integr. method Numerical integration method. •.
Show values ? Shows the graph coordinates; test level.

Numerically integrates user's data given in columns in a text-style file (such as a '.csv' file). It is assumed that:  the 1.st column contains the independent variable, X, with equally spaced values;  and the 2.nd column contains the dependent variable, Yk, with k = 1..m, the column to be integrated. (More columns can be given, 'kol' ≥ 2 being used.) Iff Δx = 0, the 1.st column is read to compute the true value.

The integration is done by the trapezoid or by the Simpson's rule.

An example 'csv' user file is given here (giving 110.555 trap., 110.5502 Simp.) or here. [The decimal mark can be point ("international") or comma ("European").] ("% Error:" messages: 2, file too large; 4, no file uploaded.)

Plots the given yk and the numerical integral Yk vs the abscissa k = 1..m.

Other suggested data: other columns (3–5) of the example file).

References: Plate: NumericalIntegration

• Wikipedia: "Numerical integration" • Search "PHP file upload" • IBM: The right way to read files with PHP

• Wikipedia: "Decimal mark" (Decimals). Byte order mark (If "BOM" is present, the innocuous characters "" will appear in the header.) • W3C: character entity reference chart.

• 1596-03-31: Descartes, René (1650-02-11).

 
 
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Created: 2015-03-31 — Last modified: 2015-04-02