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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: : 

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! : 

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]

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