Integrating x²

4/30/98

Here is a scan of a paper I wrote in 4/30/98 that I am particularly proud of. It was for a Calculus 2 class, showing how to integrate f(x) = x² using basic principles.

I am proud of this paper, because at the time, I remember it was really difficult and mysterious still, and obtaining the correct answer took quite a bit of work.

If you're not familiar with integration, it is essentially finding the area underneath a curve. If you know how to find the area of a rectangle (and you do, just base*height), you know how to integrate, in principle. The calculus way just lets the number of rectangles become infinite, and therefore the rectangles get skinnier and skinnier, and adds up the areas of all these rectangles.

Now, ~20 years later, this type of mathematics is quite simple for me. I always thought it is funny how math works like that. I hope you enjoy the paper.