6.3 Volumes of Revolution: Cylindrical Shells

OpenStax Calculus Volume 1 — Section 6.3

Learning Objectives

  • Derive the shell method formula: \(V = 2\pi \int_a^b x \cdot f(x) \, dx\)

  • Determine when shells are preferable to disks/washers

  • Set up shell integrals for revolution about the y-axis

  • Apply the shell method for revolution about vertical and horizontal lines other than the axes

Key Concepts

To be filled during study.

Practice Problems

To be completed with textbook exercises.

Section Summary

To be written after completing the section.

Study Notes

Personal observations and connections to engineering work.