Why do they teach integration and derivatives in high school? What is its use in day-to-day life?
This question, and a million others like it, should win some sort of award for the most perennial, persistent, insistent, consistent, constant conundrum among Quora queries.
I find that sad.
Question back to you: what, exactly, do they teach you in high school that *is* used in “day-to-day life”? Do they teach you to drive a car, shop at the mall and manage your Netflix queue? I’d like to believe that they teach you some world history, some literature, some geography, some linguistics, some science, perhaps a dash of music? Arts? Hm? A sprinkling of philosophy? Have you been using these things in your day-to-day life?
“Oh! But reading is important!” Sure. Then read. You could read since you were, what, seven years old?
“Oh! But history and geography are useful for following the news!” Sure. You could get everything you need to follow the news in thirty minutes with Wikipedia. High school is, what, four years?
“Oh! But chemistry and physics and biology are important! For day-to-day! Life!” Really? Are they? When was the last time you needed to calculate the trajectory of a planet, or observe the way mRNA guides the production of proteins in the cell? Have you used your deep knowledge of balancing chemical reactions while cooking?
“Yes! That’s the point! Nothing in high school is useful for real life! It’s a total waste of time!” Or, maybe, the purpose of high school isn’t to teach you daily skills?
“Alright, not daily skills, but… a career! A life! I want to be ready for real life and high school isn’t helping!”
Oh, yes it does. And besides, a career isn’t everything in life.
Your teachers don’t know what you’re going to pursue as an adult. You don’t either. Perhaps you think you know, and maybe you’re right, but maybe not. The smartest thing you can do at your age is learn as much as you can, absorb as much as possible, and be ready for whatever the future holds. Learning is a wonderful thing.
You think your future has nothing to do with integration and differentiation? Perhaps that is so. But if your future has anything to do with science, engineering, economics or modern “knowledge work” then you will need a degree in some STEM field, and that will contain a healthy amount of integrating and differentiating.
And if not?
Then your well-trained mind will be better at pattern matching, at problem solving, at wrestling with difficult but clearly-defined challenges. You’ll understand concepts and metaphors like “change of variables” or “linearity” or “extrema are stationary”, and you may be surprised by how much of a better thinker you’ll be by these.
The question suggests a very limited view of “day-to-day life”. Whose day-to-day life? What’s in a day-to-day life? Is that all you hope to do in life, live day-to-day? Eat, sleep, watch sports? No, I know. You have dreams – to succeed, to create, to do well, to have some sort of impact.
So learn more than you think you need, not less. Read poetry, to be a better programmer. Do athletics, to be a better investor. Play an instrument, to be a better parent.
And, yes, struggle with those differential calculus problems. Those are exercises for your mind. Doing burpees isn’t great fun either, but it’s good. Minimally, it’s the same thing. Possibly, those integrals will serve you immensely well.
And finally, career isn’t everything. It may take a long time, it may never happen, but you may discover at some point that you simply enjoy math. Some things don’t come easy, but when you master them they become joyful. Some people can’t imagine their life without the beauty of math. You may or may not be one of them, but without the initial work, you will never find out.
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