This is a collection of visualization tools for teaching and learning about computing volumes in calculus via application of the definite integral. Most of these tools are in the form of animated graphics stored in two formats: animated gifs for ease of use in a browser; and Quicktime movies (which require a free plugin) for greater control by the user. The animations are static in the sense that the user cannot change parameters for the curves, but an adequate sample of different curves is given for these to be effective demonstrations of the general idea of computing volumes by integration. This also has the advantage of being downloadable for use away from an Internet connection. Specific methods (disk, washer, shell) for computing volumes are given their usual special treatment, so these pages match the standard calculus textbook treatment of volume very well. The animations are fully supported by background material so that students will find on these same pages explanatory text and graphics for all ideas. Moreover, the authors have packaged the pages in a way that makes them easy for teachers to use, with clear objectives, instructor's notes, references and recommended activities supplementing every concept. This collection is a valuable tool for teachers and students of calculus, and it is part of the larger collection, Demos with a Positive Impact, organized by these same two authors.

Open Visualization for Volumes of Solids in a new window

David Hill, Lila Roberts, "Visualizations for Volumes of Solids in Calculus - Editorial Review," *Convergence* (June 2004)