Topic 35 Average Value of a Function & the Mean Value Theorem for Integrals = Stewart 6.5 Average Value = AP Classroom 8.1

I will go over the last days of homework first, but I am hoping we can move on to this. It's a simple, common-sense idea that doesn't require any "new" procedures.

Lesson Summary: finding the average value of a function over an interval. Some people think of this as the "Mean Value Theorem" for integrals. Most people find this concept fairly straightforward -- the phrase to remember is "Integral divided by Interval." 🤓 It looks like this:

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Avoid the common error: students frequently make a "linkage error" on the AP test by forgetting to write $LaTeX: \frac{1}{b-a}$ in front of the integral while working an average value problem. They then remember they need it after calculating the net change, . . . and divide the result by (b-a) but without dividing by (b-a) on the integral side of the equation. . . . and they lose a point (or more). Moral of the story: don't write math that isn't true! If you catch yourself in an error, fix it throughout the problem.

Action Items:

1. If absent, take notes either from my notes or the powerpoint & notes below -- or watch the AP videos and annotate those. Make note of any questions you may have that arise from attempting homework.

2. HW: 6.5, p. 453 #2, *5, *7, 9, *12; 15-16; 18-19. *Use a calculator as needed!

3. Extra Practice (optional): WaMap assignment 4.3 (Average Value and FTC 2)

4. Highly recommended: watch and annotate the AP Classroom videos for 8.1

Resources:

My Notes from 2021
Topic 35: The Average Value of a Function and the Mean Value Theorem
Topic 35: The Average Value of a Function and the Mean Value Theorem Notes (optional)
AP Classroom Daily Videos: 8.1 (2 videos); note: they use a technique (u-substitution) that we don't know how to do yet; don't worry about those examples. We are learning substitution beginning tomorrow!

Homework Solutions