5.3 The Fundamental Theorem of Calculus

OpenStax Calculus Volume 1 — Section 5.3

Learning Objectives

  • State FTC Part 1: \(\frac{d}{dx} \int_a^x f(t) \, dt = f(x)\)

  • State FTC Part 2: \(\int_a^b f(x) \, dx = F(b) - F(a)\) where \(F' = f\)

  • Apply FTC Part 1 to differentiate integral functions (including chain rule variations)

  • Apply FTC Part 2 to evaluate definite integrals using antiderivatives

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.