# Properties of Definite Integrals

## Lecture Notes

#### Rules for Riemann Integrals

PDF
Section 5, Page 5

Basic rules for evaluating Riemann integrals.

Instructor: Prof. Jason Starr
Prior Knowledge: The Riemann Integral (section 4 of this lecture)

#### Dummy Variables

PDF
Section 1, Page 1 to page 2

Use of dummy variables in computing Riemann integrals.

Instructor: Prof. Jason Starr
Prior Knowledge: Riemann Integral (section 4 of lecture 14)

#### Variable Limits of Integration

PDF
Section 2, Page 2 to page 3

Evaluating integrals with variables in the limits of integration. Includes example.

Instructor: Prof. Jason Starr
Prior Knowledge: Riemann Integral (section 4 of lecture 14) and Fundamental Theorem of Calculus (section 3 of lecture 15)

#### Integrating Backwards

PDF
Section 6, Page 5 to page 6

Integral from a to b equals the negative of the integral from b to a.

Instructor: Prof. Jason Starr
Prior Knowledge: Riemann Integral (section 4 of lecture 14) and Fundamental Theorem of Calculus (section 3 of lecture 15)

#### Properties of Integrals

PDF
Section, Page 1 to page 2

Definitions, including the properties of linearity, interval addition, estimation, and integrating backwards. Also includes several examples, the absolute values property, and the change of variables formula.

Instructor: Prof. David Jerison
Prior Knowledge: None

## Online Textbook Chapters

#### Always Integrable Functions

Document

Functions that are continuous or bounded increasing or bounded decreasing will always be Riemann integrable.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Riemann Sums (OT20.2)