The Riemann.m package The package can be loaded by typing "< Automatic},{Subintervals -> 25, Height -> Random}] If you want to enter only PlotRiemann options, you must insert an empty list for the plot options. Example: PlotRiemann[e,{x,1,5},{},{Partition -> Random, Mesh ->0.3}] Type ?PlotRiemann to get a description of all the options. ------------------------ RiemannSum returns only the value of the sum and does not show the graph. It takes all the PlotRiemann options. Try RiemannSum[e,{x,1,5}] ------------------------ RiemannSumList[expression,range,n] returns a list consisting of n pairs of numbers. Each pair consists of the mesh and the value of a random Riemann sum for the given expression and range. By plotting this list, you can see how the value of the sum is more accurate when the mesh is smaller. The mesh is plotted on the horizontal axis and the value of the sum on the vertical axis. Try the following, which takes about 45 seconds on a 486 Windows machine (2 to 4 times longer on 386's and older Macintoshes). RiemannSumList[e,{x,1,5},200] // ListPlot ---------------------------- The package was produced with the support of the Consolidated Natural Gas Corporation. Thanks to John Gray. Author: Charles Wells Department of Mathematics Case Western Reserve University Cleveland, Ohio 44106-7058 216-368-2893 cfw2@po.cwru.edu Copyright 1992 by Charles Frederick Wells. Rights to the material in this package are reserved. Permission is hereby granted to make copies of this file for any purpose other than direct profit or as part of a commercial product, provided that this copyright notice is retained.