6.2 Antidifferentiation by Substitution

Quick Review

What you’ll learn about Indefinite Integrals Leibniz Notation and Antiderivatives Substitution in Indefinite Integrals Substitution in Definite Integrals Essential Question What are some antidifferentiation techniques and how can I use substitution to find indefinite or definite integrals?

Indefinite Integral The family of all antiderivatives of a function f (x) is the indefinite integral of f with respect to x and is denoted by If F is any function that then where C is an arbitrary constant called the constant of integration. Example Evaluating an Indefinite Integral

Properties of Indefinite Integrals Power Functions

Trigonometric Formulas Exponential and Logarithmic Formulas

Example Paying Attention to the Differential Find each of the following antiderivatives in terms of x.

Example Using Substitution

Pg. 337, 6.2 #1-45 odd

6.2 Antidifferentiation by Substitution

What you’ll learn about Indefinite Integrals Leibniz Notation and Antiderivatives Substitution in Indefinite Integrals Substitution in Definite Integrals Essential Question What are some antidifferentiation techniques and how can I use substitution to find indefinite or definite integrals?

Example Setting Up a Substitution with a Trigonometric Identity

Example Evaluating a Definite Integral by Substitution

Example Setting Up a Substitution with a Trigonometric Identity

Pg. 338, 6.2 #47-69 odd