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| View Original: | Reciprocal integral.svg (182x174) | |||
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| Keywords: Reciprocal integral.svg en 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-the-natural-logarithm-of-x/ 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 2<sup>k</sup> is k times the integral 1 to 2 just as ln 2<sup>k</sup> k ln 2 Source used to generate this chart is shown below own User Dcoetzee 2013-03-22 Cc-zero Source All source released under CC0 waiver Mathematica source to generate graph which was then saved as SVG from Mathematica <pre> 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 -> Tablei i 0 8 Tablei 0 3 i 0 8 </pre> Axis fonts were converted to Liberation Serif in Inkscape and the graphic above the plot was added in Inkscape Hyperbola rational function Integral calculus | ||||
