Properties of Definite Integrals

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Presentation transcript:

Properties of Definite Integrals Implicit Differentiation Properties of Definite Integrals Local Extreme Points

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. Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Properties of Definite Integrals Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Properties of Definite Integrals Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 1 Evaluate the definite integral Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 2 Evaluate the definite integral Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 3 Use the definite integral to find the area between the x-axis and over the interval Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 4 Evaluate the definite integral for Implicit Differentiation Properties of Definite Integrals Local Extreme Points

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. Implicit Differentiation Properties of Definite Integrals Local Extreme Points