The only way I found to get the full text was to pay $38.
Too bad. All I can ascertain from the quality of the abstract (very poor from a myriad of angles, aside from the fact that this form of numerical integration was standard practice before the mid-18th century), is that this particular journal has much lower standards than the more prestigious ones I am familiar with. This is not necessarily a terrible thing, but I’m used to there being many below-journal-level avenues for distributing “helpful tips in the field of study”.
Not quite. Trapezoidal approximations are the methodology, not the problem. I’m not going to claim that this is a great paper, or that it isn’t an indication that there’s some serious interdisciplinary communications problems, but it’s not as immediately dismissible as the average reader might think.
Incidentally, the paper itself is sixteen years old and the blog entry that people are linking to is almost four. I wonder why we’re seeing it now.
I mentioned that in the OP. Twice, in fact, if you read through the full citation I provided. 
I got a link directly to the paper from the /r/math subreddit. This thread, to be specific, which contains this non-mathematical integration strategy:
I don’t know where the submitter on reddit got it from. Might be worthwhile to ask.
Incidentally, /r/math is also where I found TeX the World, which automatically parses LaTeX equations surrounded in special markup regardless of where on the Web it appears. Very useful.
Maybe the point of this paper is to enable people who don’t know calculus to solve the problem.
Useful doesn’t even cover [;\epsilon;] of it.
There is a medical problem which involves a curve. We want to know the area of the curve. There are a number of mathematical methods to find that out. The medical nature of the curve is totally irrelevant for the area. Using most of the space to describe the calculation makes this essentially bad mathematics.
This is similar to saying “this particular scientific problem is best described using computer software like Word instead of old-fashioned mechanical type-writers”.
We live in times when science and scientific community has expanded vastly. The reality of that sort of situation is that there will be evitavly less talented people involved. I’ve heard that 80% of professional scientists of all times are alive. I don’t know if that’s true but the scale of recruiting effort is such that we’re bound to see more papers like this.
Somebody has posted this to Slashdot: Medical Researcher Rediscovers Integration - Slashdot
Slashdot links to this article where somebody noticed the paper in 2007: Medical researcher discovers integration, gets 75 citations | An American Physics Student in England
Here is an account of an even less useful academic paper, from the Journal of Applied Behavior Analysis.
It served its purpose as far as I’m concerned. ABAs always seemed like a serious bunch, who knew they had a sense of humor?
Edit: Here’s the original: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1311997/pdf/jaba00061-0143a.pdf
I have read the paper and it doesn’t get any better. The ‘true’ value is calculated by drawing the curve in a graph paper and then counting the little squares. I am not joking here. I don’t know if I should be laughing, be mad or scared with this.
Eeek! Zombie!!
It’s not that bad a zombie, compared to threads I’ve seen resurrected.
I apologize for walking around with hands extended screaming ‘braaaiiiiins’ but I thought I gave an answer to an open question to this thread! 
If we minded, the thread would be close. Some just love zombie jokes.
You know what really makes this stand out, to me? The midpoint method is, if anything, even simpler than the trapezoid method for finding areas under curves. And for most curves, it’s about twice as accurate as the trapezoid method. That’s right: Not only did the author of this paper claim as his own a method that’s centuries old and known to anyone who stayed awake in high school math class, but the unoriginal method he stumbled upon is actually worse than the simplest possible method.