I think this diabetes doctor just tried to rename integral calculus after himself.pic.twitter.com/vU0nvrqei8
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You can't integrate if it doesn't follow a formula, yeah? And unless I'm crazy not all curves do, certainly not formulas that you can determine? Might be wrong there, haven't taken calculus in a long time
I think you're asking "Given any continuous function, will it always have an equation?". The answer is "no". That's not because of calculus per se, but because the number of equations we can write down is, in a sense, smaller than the number of continuous functions.
Okay, sure. If you don't mind explaining further, if you can't describe a curve - and IIRC it can be hard to determine that description even when it does exist - doesn't that mean you can't find the derivation and thus perform the calculus integration?
but that's just a standard rectangular approximation like you'd learn in any pre-calc clas, isn't it? lol
that's effectively a trapezoidal approximation, then. still no integral calculus
In the paper she suggests you eventually shrink the width of the intervals you consider. Taking the limit of this shrinking process (where you eventually get an infinite number of such rectangles/trapezoids) is one way to define what a definite integral is.
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