2019 CED Unit 8: Applications of Integration

This unit seems to fit more logically after the opening unit on integration (Unit 6). The Course and Exam Description (CED) places Unit 7 Differential Equations before Unit 8 probably because the previous unit ended with techniques of antidifferentiation. My guess is that many teachers will teach Unit 8: Applications of Integration immediately after Unit…

Subtract the Hole from the Whole.

Sometimes I think textbooks are too rigorous. Behind every Riemann sum is a definite integral. So, authors routinely show how to solve an application of integration problem by developing the method starting from the Riemann sum and proceeding to an integral that give the result that is summarized in a “formula.” There is nothing wrong with…

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…