Chapter 07 Reimann Sum Simulation

Description:  This simulation shows the constant-width left, right, and mid-Reimann sum of several typical integrands.  One can witness how the three methods work differently and also see the influence of the number of segments on the value of an integral.

Keywords:  Integration, numerical integration, Reimann sum.

Learning Objectives:  After successful completion of running the simulation with proper questions asked by the instructor, the student would be able to 1) graphically know the Reimann sum method of numerically integrating a function, 2) note the influence of the number of segments on the true error, 3) differentiate between the true errors obtained using the different types of Reimann sums.

Full Resources:  The full resources for the topic include textbook content,  PowerPoint presentations, multiple-choice tests, audiovisual lectures, and application examples.

Software Requirements:  Latest versions of Safari,  Microsoft Edge, Firefox, Google Chrome.

Credits:  Design Team: Autar Kaw and Mayank Pandey.  Software development: Mayank Pandey and Autar Kaw.
We acknowledge the immense help of the PhetSims Google group, third party libraries: almond-0.2.9.js, easing-equations-r12,FileSaver-b8054a2.js, fontawesome-webfont-3.0.2.svg, jama-1.0.2, jquery-2.1.0.js, lodash-2.4.1.js, pegjs-0.7.0.js, seedrandom-2.4.2.js, text-2.0.12.js, Tween-r12.js

Acknowledgments: This material is based upon work supported partially by the National Science Foundation under Grant Number 2013271. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

All Simulations: Here is the link for all the simulations developed.