Visualizing Solid Figures 2

You have probably caught on by now that Winplot is my favorite computer graphing program. In addition to being great at drawing a quick graph, it is able to produce and rotate 3D images of, among other things, solids of rotation, and solids with regular cross-sections. In this post I will discuss how to do…

Visualizing Solid Figures 1

The shape of various solid of rotation and solids with regular cross-sections of which beginning calculus students are required to find the volume are often difficult to visualize. This post and the next two will discuss some of the ways you can help your students become familiar with these shapes. Teachers often use these as…

Improper Integrals and Proper Areas

A few years ago on the old AP Calculus discussion group a teachers asked a question about this improper integral:   His (quite perceptive) student pointed out that the range of the inverse tangent function is arbitrarily restricted to the open interval . The student asked if some other range would affect the answer to…

AP Accumulation Questions

Accumulation 2: AP Exam Rate/Accumulation Questions I assume that a number of my readers are AP Calculus teachers. In following up my last post on accumulation, today I’m going to discuss a very common type of AP Calculus exam question, the rate question which is loaded with accumulation ideas. The three posts following this one…

Area Between Curves

Applications of Integration 1 – Area Between Curves The first thing to keep in mind when teaching the applications of integration is Riemann sums. The thing is that when you set up and solve the majority of application problems you cannot help but develop a formula for the situation. Students think formulas are handy and…