Topic 37 The Substitution Rule = Stewart 5.5 The Substitution Rule = AP Classroom 6.9

Lesson Summary: the substitution rule allows us to recognize when an integral is the result of having used Chain Rule during differentiation. You are looking for a function and its derivative (or a constant multiple of the derivative) inside the integrand.

Action Items:

1. More notes, in case I am still absent (hopefully I will be back). My notes include more difficult examples than yesterday's notes.

2. Book Practice: 5.5.2, p. 413 #5.5.2: #51-68 all (by hand); 75, 79, 81 (USE THE GC!); 85 & 86. This is a long assignment, but take it slow and do as much as possible. Probably not ideal to do it in one sitting, and DEFINITELY not ideal to wait until Sunday at midnight to start!

3. Extra Practice (optional): WaMap, assignment 4.4 (Integration by Substitution).

4. Highly recommended: watch and annotate the AP Classroom videos for 6.9

Resources:

My Video Notes from 2021, Day 2
Khan Academy U-Substitution Unit
Topic 37: The Substitution Rule
Topic 37: The Substitution Rule Notes (optional)
AP Classroom Daily Videos: 6.9
Stewart, Chapter 5, Section 5
Homework Solutions