The Definite Integral and the FTC

The Definition of the Definite Integral. The definition of the definite integrals is: If f is a function continuous on the closed interval [a, b], and   is a partition of that interval, and , then The left side of the definition is, of course, any Riemann sum for the function f on the interval [a,…

Good Question 7 – 2009 AB 3

Another in my occasional series on Good Questions to teach from. This is the Mighty Cable Company question from the 2009 AB Calculus exam, number 3 This question presented students with a different situation than had been seen before. It is a pretty standard “in-out” question, except that what was going in and out was money.…

Proof

When math books present a theorem they almost always immediately present its proof. I tend to skip the proofs. I assume they are correct. I want to get on with the ideas in the text. Later I may come back and read through them. Is this a good thing to advise students to do? I…

More About the FTC

In keeping with my idea from the last post of sneaking up on ideas, here is a way to sneak up on the other part of the FTC. Consider these three functions F1(t) = 3, F2(t) = 2t and F3(t) = 2t + 3 For each of these three functions do the following: Graph each…