Properties of Definite Integrals

 

Rules for Riemann Integrals

Basic rules for evaluating Riemann integrals.

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Dummy Variables

Use of dummy variables in computing Riemann integrals.

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Variable Limits of Integration

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

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Integrating Backwards

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

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Properties of Integrals

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.

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Always Integrable Functions

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

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Non Integrable Functions

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

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