Chapter 8: Integration

The definition of integration is quite complicated and we devote some time to studying that. We identify a class of "integrable" functions wihich is analogous to the "differentiable" functions of Chapter 4, and show that all continuous functions are integrable. Evaluating the integral based on the definition alone is very hard, so we prove the Fundamental theorem of calculus; the theoretical tool which is the basis of all the integration techniques in calculus. We then develop a more general theory of integration called Riemann-Stieltjes integration. This enables us to unify integration and summation; something which is useful in applications in mechanics and statistics, to name two.

Chapter Contents

Class 50
- The Definition of the Riemann Integral
Class 51
- Properties of the Integral
Class 52
- Evaluating the Integral
Class 53
Class 54
- Riemann-Stieltjes Integration
Class 55

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1996 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: June 1996