6.2 Determining Volumes by Slicing

OpenStax Calculus Volume 1 — Section 6.2

Learning Objectives

  • Compute volume by integrating cross-sectional area: \(V = \int_a^b A(x) \, dx\)

  • Apply the disk method for solids of revolution: \(V = \pi \int_a^b [f(x)]^2 \, dx\)

  • Apply the washer method: \(V = \pi \int_a^b \left([R(x)]^2 - [r(x)]^2\right) dx\)

  • Set up integrals for revolution about horizontal and vertical 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.