My Most Controversial Integral

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#math #brithemathguy #integral

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[bigbrewer]

engineers are smiling and this video while mathematicians are dying inside

[xinpingdonohoe]

I figured that if the integrand is basically 0 if you set dx=0, then it should be fine.
f(x) dx → f(x)×0=0
x^dx -1→ x^0 -1=1-1=0
sin(x) sin(dx) → sin(x) sin(0)=0

Furthermore, if you want a nontrivial solution, the strength of the differentials must be the same as the number of integrals. Each differential undoes an integral.

∫∫∫x dx² has not enough dx terms, so this "sum" would be ∞, if anything.
∫∫x³ dx⁴ has too many dx terms, so it just becomes 0.
∫cos(x) dx has just the right strength, so you'll get something not forcibly 0 or ∞.

[snuffybox]

Is there any explanation for why dx^2 should be treated like 0? The "its super small trust me" explanation doesn't quite do it for me.

[woahdotoah]

dubious maths is dubious, but its still maths.

[ankitbhattacharjee_iitkgp]

I showed this to one of my friends whose world was Mathematics. He was furious, and said to me, "If there's no dx multiplied then how do I know respect to what I integrate!?"

[ozargaman]

The (dx)ⁿ=0 while n>1 is actually correct (sort of), but that explanation is skipping a ton of steps.

[RomanNumural]

2:24 In stochastic calculus they define something called quadratic variation. A theorem is that if your function is deterministic then its quadratic variation is 0, if the function is stochastic then its first order variation is infinite. I think this is similar.

[briancoyle]

This is literally the solution I came up with too😳

I went back to watch your old video but before I played it, I tried solving it on my own and this is the solution I came up with! Although I looked at it through a slightly different perspective by incorporated elements of nonstandard calculus into my thought process. When I saw your old video I thought, oh cool a different solution but came up with same result. And then I see this video and you have the solution I came up with!

[aaronspeedy]

Why not just derive it from the limit of the finite sum? This seems like the most natural way to find this imo

[Ramasani-urdr]

Everyone talking about advanced stuff while me not understanding a single thing and getting confused by weird symbols: 😅😅😅😅🤣

[decare]

I think this can be made rigorous with a broader definition of an integral, using nonstandard analysis.

[gregstunts]

This actually does make sense on a conceptual level. You’re still taking an infinite sum, you can still approximate the integral in similar ways to normal ones. By taking small values of dx, and by using a finite sum.

[Loomr]

Perhaps, if you convert the last step before integration to a Riemann sum, then dx^k approaching zero becomes more well defined. Also, minor nitpick, but maybe you could add parenthesis to the integral to include the minus one term.

[Hadar]

I don't buy your argument, that you can just drop infinity elements of the series, because they are close to zero. In my mind you only found integral of a lower bound of the expression.

[ElderEagle]

Make a video about deriving the cubic formula

[張謙-nl]

Every time when we try to use different ways to solve those non-sense problems and always get the same result makes me wonder if there's something more fundamental that governs all theories and theorems

[JakubS]

why did you make them go to 0? Couldn't you do a double integral, then a triple integral, and so on until it converges to a specific function?

[Sofia]

Can you please do a video about the partial differential

[n.n]

If dx is so small that you treat it like 0 with the rest of the exponents, shouldn't (ln(x) * dx) ^ 0 be similar to 0^0? Why 1?

[wandrespupilo]

why are dubious methods so unreasonably effective wtf