Calculus: Volumes of Solids, Areas, Arc Length, Surface Area, Average Value





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Published on Feb 12, 2013

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 ntegration 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 (circular, equilateral, square, diamond, isosceles, rectangular)
- rectangular sections can have height as a function or as a constant

Areas under and between curves
- Riemann Sums (LRAM, RRAM, MRAM, Trapezoids)
- Integral
- Average value of a function

Arc length
Surface area

This uses Geogebra 5.0 3D. Unfortunately this version of Geogebra does not support applets, so this cannot be made available in a web browser.

I have also created a version with the same features but it can generate curves from tabular data points and various regression options.


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