# More with Def Ints

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## Presentation Transcript

### Integral Properties / U – Substitution for Definite Integrals :

Integral Properties / U – Substitution for Definite Integrals

### Objectives :

Objectives SWBAT… Use the properties of definite integrals to manipulate definite integrals Use u-substitution to find definite integrals that require a reverse chain rule Find the average value of a function on a given interval

### Docket :

Docket Review Properties of Integrals U-Substitution Average Value

### Docket :

Docket Review Properties of Integrals U-Substitution Average Value

### Definite Integrals :

Definite Integrals a b

Example:

### Docket :

Docket Review Properties of Integrals U-Substitution Average Value

### Reverse Limits Property :

Reverse Limits Property = =

### Same Limits Property :

Same Limits Property

### Interval Union Property :

Interval Union Property Extremely Important! a b c

### Docket :

Docket Review Properties of Integrals U-Substitution Average Value

### Indefinite U Substitution Review :

Indefinite U Substitution Review

### U substitution for definite integrals :

U substitution for definite integrals

You Try!

### Docket :

Docket Review Properties of Integrals U-Substitution Average Value

### Averages :

Averages To find the average of a discrete set of numbers, you simply add up all of the values and divide by how many values you have. To find the average value of a continuous function, you take the integral of the function on the interval, and divide by the interval:

### Example: Find the average value of y=3x2 on [1,4] :

Example: Find the average value of y=3x2 on [1,4]

### Find the average value of the function below on [1,4] :

Find the average value of the function below on [1,4]