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,…

Starting Integration

Behind every definite integral is a Riemann sums. Students need to know about Riemann sums so that they can understand definite integrals (a shorthand notation for the limit if a Riemann sun) and the Fundamental theorem of Calculus. Theses posts help prepare students for Riemann sums. The Old Pump Where I start Integration Flying into…

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,…

Parts and More Parts

At an APSI this summer the participants and I got to discussing the “tabular method” for integration by parts. Since we were getting far from what is tested on the BC Calculus exams I ended the discussion and said for those that were interested I would post more on the tabular method this blog going…

Trapezoids – Ancient and Modern

The other day, in the course of about 10 minutes, I came across two interesting things about Trapezoidal approximations that I thought I would share with you. The first was a link to a story about how the ancient Babylonian astronomers sometime between 350 and 50 BCE used trapezoids to, in effect, find the area…