Integration – DON’T PANIC
As I’ve mentioned before, I try to stay a few weeks ahead of where I figure you are in the curriculum. So here. early in November, I start with integration. You probably don’t start integration until after Thanksgiving in early December. That’s about the midpoint of the year. Don’t wait too much longer. True, your kids are not differentiation experts (yet); there will be plenty of differentiation work while your teaching and learning integration. Spending too much time on differentiation will give you less time for integration and there is as much integration on the test as differentiation.
The first thing to decide is when to teach antidifferentiation (finding the function whose derivative you are given). Many books do this at the end of the last differentiation chapter or the first thing in the first integration chapter. Some teachers, myself included, prefer to wait until after presenting the Fundamental Theorem of Calculus (FTC). Still others wait until after teaching all the applications. The reasons for this are discussed in more detail in the first post below, Integration Itinerary.
Integration itinerary – a discussion of when to teach antidifferentiation.
The following posts are on different antidifferentiation techniques.
Antidifferentiation u-substitution
Good Question 12 – Parts with a Constant?
Arbitrary Ranges Integrating inverse trigonometric functions.
Integration by Parts I (BC only)
Good Question 12 – Parts with a Constant How come you don’t need the “+C”?
The next three posts discuss the tabular method in more detail. This is used when integration by parts must be used more than once. If memory serves, using integration by parts twice on the same function has never shown up on the AP exams. Just sayin’.
Integration by Parts II (BC only) The Tabular method.
Parts and More Parts (BC only) More on the tabular method and on reduction formulas
Modified Tabular Integration (BC only) With this you don’t need to make a table; it’s quicker than the tabular method and just as easy.
Revised and updated November 4, 2018
Teaching Calculus 