Visual Calculus - Volumes and Areas

This is an application developed for an AP Calculus course. It allows students to more readily visualize volumes and areas. This application allows the user to either enter their own functions, or to choose from an extensive list of textbook questions and previous AP exam questions. It allows functions to be graphed in terms of x or in terms of y, allowing integration with respect to x or y.
  • Volumes of solids
  • Disks/Washers
  • Cylindrical shells
  • Revolution about x or y-axis or about a horizontal or vertical line
  • Sections/slices (semicircles, circular, equilateral, square, diamond, rectangular, isosceles)
  • Rectangular sections can have height as a function or as a constant
  • Areas under and between curves
  • Riemann Sums (LRAM, RRAM, MRAM, Trapezoids)
  • Integrals
  • Average value of a function
  • Arc length and surface area
This uses Geogebra 5.0 3D. You will need the latest version for this to load properly if you download it. It will probably run better downloaded. Some of the features:
  • Show Text - this will show the solution to the area or volume problem
  • Hide Volume - this will show a single section, disk, washer or shell (with disks or shells, you can then adjust theta to show the rotation)
  • Inverse - will allow functions to be graphed in terms of y instead of x
  • Rotation Shadow - shows effect of the rotation about an axis in 2D
  • Centroid - will cause sections to pass through the centroid
The example questions come from two textbook sources used in my AP Calculus course: Calculus: Graphical, Numerical, Algebraic by Finney Ross (abbreviated BB for blue book) Calculus: A FIRST Look by James Stewart (abbreviated RB for red book) Clayton Maleski