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…

Antidifferentiation

Since a lot of classes start integration with antidifferentiation, I’ll discuss that first. If you decided to go with one of the other plans mentioned in my last post, then file this away for later. ____________ The key to finding antiderivatives is pattern recognition. The simplest integrals are those that follow directly from derivatives such…

Integration Itinerary

Before I write about integration I’d like to say a few words about the order of topics. Since I assume most of you are AP Calculus teachers, the list of concepts and topics goes something like this: Area of a region between the graph and the x-axis, which leads to Riemann sums, which leads to…