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

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.
Implicit Differentiation
Properties of Definite Integrals
Local Extreme Points

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

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

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

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

7. 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

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

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.
Implicit Differentiation
Properties of Definite Integrals
Local Extreme Points