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Mean Value Theorem for Definite Integrals: Rules and Examples

Learn about the properties of definite integrals, order of integration, additivity, and average value. Explore the rules for integrating constants, multiples, and differences with detailed examples. Understand how the Mean Value Theorem applies to definite integrals, finding the average value and more.

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Mean Value Theorem for Definite Integrals: Rules and Examples

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  1. Properties of Definite Integrals 6.3

  2. Order of Integration

  3. Zero

  4. Constant Multiple

  5. Sum and Difference

  6. Additivity

  7. Intervals can be added (or subtracted.) Integrals can be added and subtracted.

  8. Max-Min Inequality

  9. Domination

  10. Rules for DefiniteIntegrals

  11. Example Using the Rules for Definite Integrals

  12. Example Using the Rules for Definite Integrals

  13. Example Using the Rules for Definite Integrals

  14. Average (Mean) Value

  15. The average value of a function is the value that would give the same area if the function was a constant:

  16. Example Applying the Definition

  17. Mean Value Theorem (for definite integrals) If f is continuous on then at some point c in , The mean value theorem for definite integrals says that for a continuous function, at some point on the interval the actual value will equal the average value. p

  18. The Mean Value Theorem for Definite Integrals

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