July 2023
Beginner to intermediate
304 pages
6h 41m
English
Content preview from Calculus II Workbook For Dummies
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Chapter 13
Pump up the Volume — Solving 3-D Problems
IN THIS CHAPTER
Using disk and washer methods to calculate volume of revolution around a horizontal axis
Using inverse functions to calculate the volume of revolution around a vertical axis
Finding the surface area of revolution
Using the shell method to find vertical volume of revolution without inverse functions
A common application of integration is finding the volume of a solid of revolution. These problems tend to come in a few main varieties, roughly sorted into three key categories: disk, washer, and shell. These methods build integrals from simple geometric formulas that enable you to accurately measure the volume of a complicated solid.
In this chapter, I first show you how to use the disk and washer methods to find the volume of a solid of revolution around a horizontal axis. Next, I show you how to use the inverse of a function when working with solids of revolution around a vertical axis.
After this, you use a formula for finding the surface area of a solid of revolution. To finish up, I show you how the shell method ...
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