Inverse Trig Functions are officially included in the AP Calculus AB curriculum, and they are covered in our textbook: Differentiation in Chapter 5.8, Integration in Chapter 5.9.
In preparing for the AP exam, students may rightfully choose to prioritize strengthening fundamental skills over learning new skills involving inverse trig.
A typical AP Calculus AB exam might only include a question or two on this topic. Even more noteworthy to me as a teacher, I don't feel that omitting this topic will significantly detract from a student's sense of understanding and appreciating the bigger picture of Calculus.
All that being said, a student who is confident in all the other topics we've studied should absolutely forge ahead and add Inverse Trig Differentiation and Integration to his/her collection of skills.
I HATE MINDLESS MEMORIZATION.
At first it may seem like mindless memorization is required in order to work efficiently with the Calculus of inverse trig functions.
In this one-page table and summary, I attempt to present an approach that requires no extra memorization.
The Shell Method for computing volumes of revolution used to be in the AP Calculus curriculum. I don't know exactly when it was removed (I found something on the Internet claiming 1997). In any case, some/many/most (?) college Calculus courses still teach the Shell Method.
You may find it in Chapter 6.3 of our textbook.
In case you're interested, here are the examples I used in class to give you a quick glimpse of the Shell Method.
Here are a final set of FRQ, both questions and solutions, that you may use to prepare for the AP Exam (Actually, get them from Mr. White since packet includes CollegeBoard content). These questions tend to have some of the lowest mean scores over the past decade or so. If you can get even half of the points, you're ahead of the pack. Most of these questions also include tables of data. Since our textbook doesn't include many such questions, it would be beneficial to make sure you're comfortable with this type of question.