Numerical Integration is a lab exploring numerical methods for computing integrals. That is, using a computer program or calculator to find an approximation to the integral of some function $f(x)$.

Of course, because we are talking about integration we can’t go very far without the fundamental theorem of calculus: $ F(x) = \int_a^x{f(t)dt} $. Further, in this lab we will talk about a few methods for numerically computing integrals, namely: Rectangle/ Riemann Sum, Trapezoidal Sum, Parabola/ Simpson’s Rule, just to name a few.

In Calculus courses, we are usually given “nice” functions, functions that are “easy” to solve or do not require numerical methods to compute. However, the set of functions that are “nice” is very small. Thus, we must resort to numerical methods. For example, there is no elementary antiderivative to the following integral:

$$ \int{e^{e^x}dx} $$

But we can approximate it using one of the methods that we explore in this lab.

I was initially drawn toward this lab because other courses have introduced numerical integration and I have used other numerical methods by hand and wanted to further explore the topic by automating it and exploring the different methods.

tylermurphyThis is an excellent concept! I haven’t had any courses where numerical integration has been introduced or even discussed. But I have often been stumped by integrals like $\int e^{e^x}dx$. I know that the number of functions is uncountable and often they are what my wife calls “horrendously evil.” To be fair, those are the ones I am most interested in and would really like to see how this lab turns out. Perhaps I’ll try this one for one of the ones left. Thanks for the introduction to it.

grantrosandickThis was the other chapter that I was debating to explore. I remember taking Calc 2 and some of those integrals were extremely difficult. You’re example using $e$ is a perfect example of one of these difficult integrals. This could be a very interesting chapter exploring these types of integrals. I’ll definitely have to contemplate doing this lab next. Great introduction.