Math 20B: Calculus 2 Handouts

On this page we have a variety of handouts. These handouts are designed to be short, one sheet of paper summaries of the most important aspects of the topic they cover, for an easy reference. Some of these handouts have practice problems with the answers listed, in case you'd like to practice! All of these handouts are also available printed in-person at the Math Learning Center.

Review Handouts

Math 20A IMPORTANT fact sheet Links to an external site.

Common graphs you must know Download Common graphs you must know

Trigonometry summary Download Trigonometry summary

Calculus 2 Handouts

Volumes of Revolutions handout Download Volumes of Revolutions handout

There's a lot going on in Chapter 6 with the disk/washer method and the shell method. Which do you choose, and how? What are the differences? This handout has the formulas for all the methods and some great, useful tips on doing volumes of revolutions problems.

Integration Summary Sheet Download Integration Summary Sheet

This sheet has everything you need to know about integration, including how to do every chapter 7 technique.

7.4 - Partial Fractions handout Download 7.4 - Partial Fractions handout

7.8 - Improper Integrals handout Download 7.8 - Improper Integrals handout

Series Tests Download Series Tests

Here's a list of all series tests for your reference. For all tests, you must check all the hypotheses (conditions) they require. So to use an integral test, you must not only compute the appropriate improper integral, you must first check if the function is positive, continuous, and decreasing.  I emphasize that in order to use a Comparison test, the sequences must be positive. 

Always make sure you when you are doing a series test, you write a clear conclusion that states which series is converging or diverging, and why (which test is determining this). I don't give any credit for saying "it converges." In a comparison test, you actually have two series, and then you're comparing something about the two sequences. Any one of these four can converge or diverge, so make sure you are specific.

Series Test Flowchart Download Series Test Flowchart

Of course, a huge problem students always ask is how do they choose which test to use? Here's a high quality, not at all pretty looking, flowchart that can help you find that answer.

Common Maclaurin Series Download Common Maclaurin Series

Formulas for Parametric and Polar Curves, Polar Graphs.pdf Download Formulas for Parametric and Polar Curves, Polar Graphs.pdf

Polar Graph Paper Download Polar Graph Paper