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File:Reciprocal integral.svg

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Summary

DescriptionReciprocal integral.svg
English: A plot giving some geometric intuition for why the integral of 1/x is ln n, based roughly on an explanation from "Why is the integral of 1/x equal to the natural logarithm of x?". The integral from 1 to 2 is equal to the integral from 2 to 4 and the integral from 4 to 8. Each region is similar to the last except that it has been scaled vertically to 50% its previous height, and scaled horizontally to 200% its previous width. Extending this, the integral from 1 to 2k is k times the integral 1 to 2, just as ln 2k = k ln 2. Source used to generate this chart is shown below.
Date
Source Own work
This W3C-unspecified diagram was created with Mathematica.
Author User:Dcoetzee

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Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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Source

All source released under CC0 waiver.

Mathematica source to generate graph (which was then saved as SVG from Mathematica): 

Plot[][{{1/x, 1 < x < 2}}],
 Piecewise[{{1/x, 2 < x < 4}}],
 Piecewise[{{1/x, 4 < x < 8}}]},
 {x, 0, 8.5}, PlotRange -> {0, 2.1},
 Filling -> {{2 -> Axis}, {3 -> Axis}, {4 -> Axis}},
 LabelStyle -> {FontSize -> 14},
 AspectRatio -> 0.9,
 Ticks -> {Table[i, {i, 0, 8}], Table[i*0.3, {i, 0, 8}]}]

Axis fonts were converted to Liberation Serif in Inkscape, and the graphic above the plot was added in Inkscape.

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Date/TimeThumbnailDimensionsUserComment
current23:58, 22 March 2013 Thumbnail for version as of 23:58, 22 March 2013 183 ×ばつ 175 (47 KB)Dcoetzee == {{int:filedesc}} == {{Information |Description ={{en|1=A plot giving some geometric intuition for why the integral of 1/x is ln n, based roughly on an explanation from [http://arcsecond.wordpress.com/2011/12/17/why-is-the-integral-of-1x-equal-to-...

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Width182.69922
Height174.74419

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