AP Calculus AB Chapter 4 Section 5 Integration

AP Calculus AB Chapter 4, Section 5 Integration by Substitution 2013 - 2014

Pattern Recognition �In this section, we will work on finding definite integrals for composite functions using usubstitution. �This is similar to chain rule for derivatives. �Derivative example:

The goal: �Find something that looks like a function in a function. �Find something that looks like it is a derivative of something else in the integral.

Antidifferentiation of a Composite Function �

Recognizing Patterns �

Fitting the Pattern �

Multiplying and Dividing by a Constant �

Change of Variables �

Change of Variables �

Change of Variables �

Change of Variables �

Guidelines for Making a Change of Variables �

The General Power Rule for Integration �

Substitution and the General Power Rule �

Substitution and the General Power Rule �

Substitution and the General Power Rule �

Substitution and the General Power Rule �

Substitution and the General Power Rule �

Change of Variable for Definite Integrals �

Change of Variables �

Change of Variables �

Integration of Even and Odd functions �

Integration of an Odd Function �

Ch. 4. 5 Homework �Pg. 304 – 306, #’s: 1 – 37 every other odd, 43, 47, 65, 71, 75, 83, 89, 99