Integration and Accumulation of Change – Unit 6

Unit 6 develops the ideas behind integration, the Fundamental Theorem of Calculus, and Accumulation. (CED – 2019 p. 109 – 128 ). These topics account for about 17 – 20% of questions on the AB exam and 17 – 20% of the BC questions. Topics 6.1 – 6.4 Working up to the FTC Topic 6.1…

Integration

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…

Good Question 13

Let’s end the year with this problem that I came across a while ago in a review book: Integrate  It was a multiple-choice question and had four choices for the answer. The author intended it to be done with a u-substitution, but being a bit rusty I tried integration by parts. I got the correct answer,…

Antidifferentiation

We now turn to integration. The first thing to decide is when to teach antidifferentiation. 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. Still others wait until…

Integration by Parts 2

Sometimes when doing an Antidifferentiation by Parts, the resulting integral is simpler than the one you started with but requires another, perhaps several more, antidifferentiations. You can do this but it can get a little complicated keeping track of everything especially with all the minus signs. There is an easier way. Let’s consider an example:…

Integration by Parts 1

The antidifferentiation technique known as Integration by Parts or Antidifferentiation by Parts is based on the formula for the Product Rule: . Solve this equation for the second term on the right: . Integrating this gives the formula . By the FTC the first term on the right can be simplified giving the formula for…