Y the FTC?

So, you’ve finally proven the Fundamental Theorem of Calculus and have written on the board: And the students ask, “What good is that?” and “When are we ever going to use that?” Here’s your answer. There are two very important uses of this theorem. First, in words the theorem says that “the integral of a…

Riemann Sums – the Theory

The series of post leads up to the Fundamental theorem of Calculus (FTC). Obviously, a very important destination. Working Towards Riemann Sums Definition of the Definite Integral and the FTC – a more exact demonstration from last Friday’s post and The Fundamental Theorem of Calculus –  an older demonstration More about the FTC The derivative of a function…

Good Question 15: 2018 BC 2(a)

My choices for the Good Question series are somewhat eclectic. Some are chosen because they are good, some because they are bad, some because I learned something from them, some because they can be extended, and some because they can illustrate some point of mathematics. This question and the next, Good Question 16, are in…

Units

I had a question from a reader recently asking about how to determine the units for derivatives and integrals. Derivatives: The units of the derivative are the units of dy divided by the units of dx, or the units of the dependent variable (f(x) or y) divided by the units of the independent variable (x).…

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,…