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…

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Applications of Integration – Area & Average Value

Usually the first application of integration is to find the area bounded by a function and the x-axis, followed by finding the area between two functions. We begin with these problems First some calculator hints Graphing Integrals using a graphing calculator to graph functions defined by integrals Graphing Calculator Use  and Definition Integrals – Exam…

Good Question 16

I had an email last week from a teacher asking, how come I can use a substitution to find a power series for  , and for  , but not for  ? The answer is that you can. Substituting (2x) in to the cosine’s series give you a Taylor series centered at x = 0, 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…

Brushing Up the Blog

Happy Thanksgiving! I’ve been working this month on making things at the Teaching Calculus blog easier to find. There are about 360 posts and it’s getting difficult for me to find things. Here is the new line up on the black navigation menu at the top of each page. Click each to see more. HOME…

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…