1. Integration by Substitution
AP Calculus
March 27-28, 2017
Mrs. Agnew

2. Essential Question Essential Vocabulary
How do you evaluate integrals using substitution?
Essential Vocabulary
Integration by Substitution
Definite Integral
Indefinite Integral

3. Integration by Substitution
So far, we have evaluated only those integrals where we could find an antiderivative using our rules.
Evaluate the following… what is the problem?

4. Integration by Substitution
Given a composite function (a “function within a function”), the antiderivative is given by…
Integration by substitution “undoes” the chain rule for differentiation.

5. Integration by Substitution
We will be making the following substitutions
u = g(x) and du = g'(x)
So rewriting the previous formula…

6. Integration by Substitution
Find the “inside” function and its derivative.
Replace the “inside” function with u and its derivative with du.
Find the antiderivative.
Replace u with the function and simplify.
CHAIN RULE IN REVERSE!
Practice: Page #2 – 29 (Every 3rd)

7. Definite Integrals
When using integration by substitution with definite integrals, you must adjust the limits of integration.
a and b are the original limits of integration
u = g(x)

8. Practice and Homework Guided Practice Homework
Page #38 – 44 (E), 50, 56
Homework
See Worksheet Provided
Homework may be collected for grade