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Summary

Description
English: Simpson’s Rule is used to numerically evaluate the integral of a function between fixed end points (denoted by and in the above diagram). The technique is as follows:
  • The function is evaluated at its end points.
  • The function is evaluated at an odd number of points equally spaced between the end points (the interpolated points). The distance between each pair of points is .
  • The area under the curve is broken down into strips, each strip having a width of . In the above diagram, each strip is denoted by a different colour.
  • The function is approximated piece-wise by a set of parabolas, one parabola for each strip. Each parabola passes through through its strip’s end points and mid-point. In the above diagram, each parabola has a different colour.
  • The area of any particular strip below the parabloa is calculated using the formula:
where is the co-ordinate of the strip's mid-point.
  • The total area is calculated by adding the areas of all the strips together. The formula for the total area is given by:
Date
Source Own work
Author Martinvl
Other versions

Some authors prefer to define as the width of the strips rather than the spacing of the interpolation points. In such cases, it is recommended that the following is used:

  • Alternative definition
  • '"`UNIQ--postMath-00000010-QINU`"' defined as width of strip
    defined as width of strip

Licensing

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w:en:Creative Commons
attribution
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Captions

Explanation of Simpsons Rule in the form of a graph for h defined as spacing of points

Items portrayed in this file

depicts

numerical integration

inception

30 April 2025

File history

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Date/TimeThumbnailDimensionsUserComment
current21:25, 1 May 2025Thumbnail for version as of 21:25, 1 May 2025559 × 376 (19 KB)MartinvlAdded extra annotation
21:24, 30 April 2025Thumbnail for version as of 21:24, 30 April 2025559 × 376 (14 KB)MartinvlUploaded own work with UploadWizard
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