# Area and Volume Problems (Type 4)

AP Type Questions 4: Area and Volume Given equations that define a region in the plane students are asked to find its area, the volume of the solid formed when the region is revolved around a line, and/or the region is used as a base of a solid with regular cross-sections. This standard application of…

# 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 integrals, part 2: Volume problems

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…

# 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…

# 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…