earthonator wrote:i couldn't find a math thread and this probably doesn't fit in the school thread so here's my question. why do integrals work?
like if im just trying to find the integral of a line with 2 points A and B, I split it up into infinitely small pieces. so how am gonna get from point A on my line to point B? I wouldn't get anywhere the pieces are infinitely small! we are now finding the volume and surface area of 3-D objects in my calc class but this one fundamental concept doesn't make sense.
also why are integrals exact answers? obviously in the real world they're all estimations as nothing is perfectly smooth. but how are integrals not estimations. when I do an integral on my calculator I know it's an estimation. it's some program doing a reimann sum. but why is it when I do it on paper manually I get an EXACT answer? this is related to my first question.
I'm scouring the web right now, reading reddit explanations and YouTube videos, maybe I'm just rubbish at googling, but it still doesn't make sense. can anyone explain this or link me to something that would help? im asking my calc teacher tommrow hopefully she'll know and not give me an answer like "wait for college"...
fun_yunchables wrote:We can find the exact value when we do it on paper, since a function is a representation of all values at all points.
earthonator wrote:also in physics we do more "application in the real world" problems so when we take the integral of something, these pieces aren't infinitely small correct? they're actually as small as an electron or quark right; they're finitely small. because nothing in the real world can be smaller than that. right?
A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness.
JewTurk wrote:Curious, for those who study math/enjoy it. What class made you fully realize how much you enjoyed it?
fun_yunchables wrote:also started an industrial research job landing people on the moon and i miss doing real math. nobody cares for proofs here
turkeyschmitt wrote:fun_yunchables wrote:also started an industrial research job landing people on the moon and i miss doing real math. nobody cares for proofs here
been working in software for 3 years since studying cs+math, and i yearn for even the idea of a proof. the work does sometimes does end up being surprisingly satisfying, but its not the same. then again, i am no way smart/dedicated enough to stay in the magical land of academia, so can't really complain. ideally i would work through some books in my free time - he says as cauchy-schwarz master class stares at him from his desk, covered in a light layer of dust and guilt...
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