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 sum) and the Fundamental theorem of Calculus. Theses posts help prepare students for Riemann sums. Integration Itinerary  Some thoughts on the order of topics…

# 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,…

# 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,…

# Good Question 12 – Parts with a Constant?

Someone asked me about this a while ago and I thought I would share it with you. It may be a good question to get your students thinking about; see if they can give a definitive answer that will, of course, include a justification. Integration by Parts is summarize in the equation To use the…