Highlights for High School Home > AP Calculus > Interpretations & Properties of Definite Integrals > Properties of Definite Integrals

Properties of Definite Integrals

Lecture Notes

Rules for Riemann Integrals

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Section 5, Page 5

Basic rules for evaluating Riemann integrals.

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: The Riemann Integral (section 4 of this lecture)
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Dummy Variables

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Section 1, Page 1 to page 2

Use of dummy variables in computing Riemann integrals.

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: Riemann Integral (section 4 of lecture 14)
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Variable Limits of Integration

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Section 2, Page 2 to page 3

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

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: Riemann Integral (section 4 of lecture 14) and Fundamental Theorem of Calculus (section 3 of lecture 15)
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Integrating Backwards

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Section 6, Page 5 to page 6

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

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: Riemann Integral (section 4 of lecture 14) and Fundamental Theorem of Calculus (section 3 of lecture 15)
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Properties of Integrals

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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.

Course: 18.01 Single Variable Calculus, Fall 2006
Instructor: Prof. David Jerison
Prior Knowledge: None
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Online Textbook Chapters

Always Integrable Functions

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

Course: 18.013A Calculus with Applications, Spring 2005
Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Riemann Sums (OT20.2)
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Non Integrable Functions

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Examples of functions that are not Riemann integrable, as well as a definition of the principle part of an integral.

Course: 18.013A Calculus with Applications, Spring 2005
Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Riemann Sums (OT20.2)
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