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Properties of Definite Integrals

Learn how to calculate definite integrals, find area under curves, and solve application problems. Dive into examples and practice evaluating integrals to enhance your understanding of properties. Discover how to apply integrals to real-world scenarios, like determining the total increase in horn length of bighorn rams over specific age intervals.

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Properties of Definite Integrals

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  1. Properties of Definite Integrals

  2. Objectives Students will be able to • Calculate a definite integral using the properties of definite integrals. • Calculate the area between a curve and the x-axis over a given interval. • Use definite integrals to application problems.

  3. Properties of Definite Integrals

  4. Properties of Definite Integrals

  5. Example 1 Evaluate the definite integral

  6. Example 2 Evaluate the definite integral

  7. Example 3 Use the definite integral to find the area between the x-axis and over the interval

  8. Example 4 Evaluate the definite integral for

  9. Example 5 The average annual increment in the horn length (in centimeters) of bighorn rams born since 1986 can be approximated by where x is the ram’s age (in years) for x between 3 and 9. Integrate to find the total increase in length of a ram’s horn during this time.

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