7.8: Improper Integrals

Action Items:

1. Notes: if you are absent, take notes on the material below as necessary then attempt the homework. If you are struggling with the topic or need a review of concepts beyond what is contained in my summary notes, refer to Stewart 7.8.

Here's a puzzler:

0 = 0 + 0 + 0 + 0 + . . .

0 = (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + . . .

0 = 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + . . .

0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + . . .

0 = 1 + 0 + 0 + 0 + 0 + . . . = 1

😳 what (if anything) went wrong?!

Today's Topic: Improper Integrals If you are struggling with the topic or need a review of concepts, refer to Stewart 7.8.

Summary of my notes:

BC 7.8: Improper Integrals Notes

BC 7.8: Integrals Comparison Test Notes

2. Practice: 7.8.2 #25, 49; 50-55 all.

Things you MUST KNOW: Convergence Tests!

Divergence Test

Harmonic Series

Integral Test

What kind of series this is: $LaTeX: a_n=a_1\cdot r^{\left(n-1\right)}$

What this is and what it means:

$LaTeX: S=\frac{a_1}{1-r}$ , when LaTeX: |r|<1

Divergence Test:

What kind of series this is: $LaTeX: a_n=a_1\cdot r^{\left(n-1\right)}$

$LaTeX: S=\frac{a_1}{1-r}$ , when LaTeX: |r|<1

Resources:

Series Homework Solutions

AP Classroom Videos:

10.4: Integral Test for Convergence (2 videos)

Or catch up with one of the previous AP videos (I highly recommend these, whether you think you fully understand everything or not!)!

10.1: Defining Convergent and Divergent Series
10.2: Working with Geometric Series
10.3: nth Term Test for Divergence