6.4 Arc Length and Surface Area

OpenStax Calculus Volume 1 — Section 6.4

Learning Objectives

  • Derive and apply the arc length formula: \(L = \int_a^b \sqrt{1 + [f'(x)]^2} \, dx\)

  • Set up arc length integrals for functions of \(x\) and \(y\)

  • Compute surface area of revolution: \(S = 2\pi \int_a^b f(x) \sqrt{1 + [f'(x)]^2} \, dx\)

  • Recognize when arc length integrals can be evaluated in closed form vs. numerically

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.