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…

Applications of Integration – Volume

One of the major applications of integration is to find the volumes of various solid figures. Volume of Solids with Regular Cross-sections  This is where to start with volume problems. After all, solids of revolution are just a special case of solids with regular cross-sections. Volumes of Revolution Subtract the Hole from the Whole and…

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 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…