"Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}\!f(x)\,dx} \int _{a}^{b}\!f(x)\,dx is defined informally as the signed area of the region in the xy-plane that is bounded by the graph of f, the x-axis and the vertical lines x = a and x = b. The area above the x-axis adds to the total and that below the x-axis subtracts from the total."
Oh, is that all!
Welcome to more of me failing to learn advanced math. Well, okay, it's not 100% accurate to say that I'm failing, but I'm being thwarted and blocked just a bit by unnecessary obtuseness such as that just quoted. I suspect that there may be a definition of definite integrals out there somewhere which is somewhat more comprehensible to people who don't already know what definite integrals are. I also suspect that communication with the general public is not a strong point among STEM (Science, Technology, Engineering and Math) nerds, and I suspect that it may not be a strong point because, generally speaking, they despise us. They don't particularly want to help. Maybe I'm completely wrong about that because what the Hell do I know about math anyway because for the last 40 years, ever since I finished 10th grade and all of the math I was ever required to study, I've been running away from math. Or maybe it's not the general public at all which nerds tend to despise, but me in particularly, because I in particular tend to offend nerds in some way.
Then again, maybe I'm right. I'm not the first to suggest such a thing. For example, some people have noticed how computers tend to be made by nerds for nerds, and not for the general public; that is to say, the general public has difficulties with computers not because these difficulties are inherent but because the nerds who made the computers don't care much, generally speaking, about the general public and its difficulties. Which is somewhat shocking when you consider that it is the general public which is directly responsible for the nerds making all of those gazillions of dollars, euros, yen and so forth. But they don't have to care because the general public has not yet caught up with the nerds enough to be able to choose the more user-friendly ones from among them, to borrow a nerdly phrase. And don't come at me with Apple, saying that Apple is that user-friendly brand of nerd right before my eyes which I refuse to see. Apple is a rip-off, and ripping people off ain't friendly.
There are not yet enough computer nerds that they have to compete with each other for the approval of the general public. 100 years ago, auto mechanics were just as smug and unbearable as computer nerds are now. A meager supply of mechanics and a huge demand for their services gave them elite status, and they abused the situation and were assholes about it, preferring to be moody geniuses rather than to be helpful and nice and have lots of friends. Then more people learned how to make and fix automobiles, and all of a sudden it wasn't an elite profession any more, and those who had so recently thought of themselves as geniuses suddenly had trouble finding work, and they had no friends to help them.
Those who do not learn from history are condemned to repeat it, STEM nerds.
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