5.1 Approximating Areas

OpenStax Calculus Volume 1 — Section 5.1

Learning Objectives

  • Use sigma notation to express sums: \(\sum_{i=1}^{n} a_i\)

  • Approximate area under a curve using left, right, and midpoint Riemann sums

  • Understand that increasing \(n\) (number of rectangles) improves the approximation

  • Recognize the definite integral as the limit of Riemann sums as \(n \to \infty\)

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.