Foreshadowing the FTC

This is an example to help prepare students to tackle the Fundamental Theorem of Calculus (FTC). Use it after the lesson on Riemann sums and the definition of the definite integral, but before the FTC derivation. Consider the area, A, between the graph of  and the x-axis on the interval . Set up a Riemann sum using…

half C

Visualizing Solid Figures 5

To end this series of posts on visualizing solid figures, we will look at a problem that relates to how volumes of solid figures are formed. It has 5 parts which will be presented first. Then the solution will be given. Consider the region in the first quadrant bounded by the graphs of the parabola…

Shell still

Visualizing Solid Figures 4

Volume by the method of “Cylindrical Shells” Today I will show you how to visualize the cylindrical shells used in computing the volume using Winplot. Winplot is a free program. Click here for Winplot and here for Winplot for Macs. For the example I will use the same situation as in the last post. This…

Washer still

Visualizing Solid Figures 3

Volume by “Washers” Today I will show you how to visualize not just the solid figures but the disks and washers used in computing the volume using Winplot. The next post will show how to draw shells. Winplot is a free program. Click here for Winplot and here for Winplot for Macs. For the example we’ll…