5.2 The Definite Integral

OpenStax Calculus Volume 1 — Section 5.2

Learning Objectives

  • Define the definite integral as \(\int_a^b f(x) \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i^*) \Delta x\)

  • Apply properties: linearity, additivity over intervals, comparison

  • Interpret the definite integral as signed area (positive above, negative below x-axis)

  • Evaluate definite integrals using geometry (areas of known shapes)

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.