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365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:52:04 | i watched the animation. | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:52:06 | But it’s hard to get to a point where you just get it, without having to go “ok I’m adding up the rate of change of the area of the rectangle, which is the same as dadada” every time | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:52:48 | @s_chanch did you watch the 3b1b video | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:53:05 | yea | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:53:08 | Personally it didn’t super help for me lol | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:53:21 | Nothing did, it’s just very unintuitive | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:54:06 | ok | 1 | 0 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:54:11 | Sorry that prob isn’t very helpful lol | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:54:14 | this theorem is *intuitively true* | 1 | 0 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:54:27 | what isn’t is *how it implies integration, differentiation are opposites* | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:54:27 | You intuitively understand why they’re inverses? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:54:54 | no | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:54:57 | this is my question | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:54:57 | Doesn’t that mean you get why they’re opposites? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:55:11 | i don’t | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:55:34 | it should be obvious for you why this theorem implies differentiation reverses integration | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:55:36 | not for me | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:55:46 | (this is the motivation for ftc2 isn’t it) | 1 | 0 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:55:53 | You mean the statement of the theorem, right? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:55:59 | no | 1 | 0 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:56:04 | i know the statement of the theorem | 1 | 0 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:56:08 | i know why it’s true | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:56:10 | i can prove it | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:56:13 | Yeah | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:56:22 | But you don’t get *why* it’s true? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:56:26 | i can’t see why it has to do with ‘diff = inverse int’ | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:56:50 | Oh | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:56:59 | Inverse function means f(g(x)) = x | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:57:01 | this statement and ftc1 are complete aliens to one another | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:57:02 | to me | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:57:33 | We’re working with “functions of functions” (I’ll call it a functional) | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:57:51 | composite functions you mean? | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 150,414,892,225,134,600 | RokettoJanpu | 01/30/2022 02:58:01 | inverses act as undo buttons | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 02:58:04 | So if f,g are functionals, then f(g(s(t)) = s(t) for any function s | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 150,414,892,225,134,600 | RokettoJanpu | 01/30/2022 02:58:30 | we start at f | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 150,414,892,225,134,600 | RokettoJanpu | 01/30/2022 02:58:35 | integrate | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 150,414,892,225,134,600 | RokettoJanpu | 01/30/2022 02:58:39 | then differentiate | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 150,414,892,225,134,600 | RokettoJanpu | 01/30/2022 02:58:51 | ftc1 says the result is f | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 420,244,167,726,333,950 | kirby your mom | 01/30/2022 02:59:08 | Wow, how helpful | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 150,414,892,225,134,600 | RokettoJanpu | 01/30/2022 02:59:12 | ie differentiation undoes integration | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 334,482,942,506,041,340 | Zybikron | 01/30/2022 02:59:22 | Start with a function $f(x) = F'(x)$. Then $\frac{d}{dx}(\int_a^xf(t)\ dt) = \frac{d}{dx}(F(x) - F(a)) = F'(x) =f(x)$ | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:59:24 | it says F’(x) = f(x), where F(x) = int f(t) dt [a, x] | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 510,789,298,321,096,700 | TeXit | 01/30/2022 02:59:25 | **Zybikron** | 334482942506041345.png | 0 | 1 | null | null | null | null | null | ||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 02:59:40 | so F is an antiderivative of f | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:00:20 | but x is just some upper bound in F’s expression | 1 | 0 | 150,414,892,225,134,600 | RokettoJanpu | 6002 | RokettoJanpu | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:00:23 | F is the antiderivative. In words, it’s literally saying “the derivative of the antiderivative is equal to the original function” | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:01:09 | so basicallt | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:01:24 | ‘antiderivative just so happens to be an integral with x acting as an upper bound’ | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:01:38 | ‘and that means integrals are heavily related to derivatives!’ | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:01:47 | Oh you’re wondering why it has those bounds | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:02:04 | Instead of saying $$F(x) = \int f(x)dx$$ | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 510,789,298,321,096,700 | TeXit | 01/30/2022 03:02:07 | **abs\_0** | 307070375735459842.png | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | ||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:02:19 | ? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:02:36 | no | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:02:48 | from this | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:02:52 | to this | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:02:54 | i don’t understand | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:03:06 | Do you understand this | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:03:26 | yea | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:03:29 | Okay | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:04:07 | The thing that links
> antiderivative is integral with upper bound stuff
to
> integrals are inverses of derivatives
is precisely the Fundamental Theorem of Calculus | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:04:21 | ???? | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:04:26 | Sorry | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:04:28 | Editing rn | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:05:59 | @s_chanch ? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:06:11 | i don’t get this | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:06:22 | You don’t get how those could be linked? | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:06:51 | (This is rhetorical, you’re not supposed to) | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:07:05 | (That’s why it’s called the fundamental theorem of calculus, why it’s so powerful) | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:07:36 | (It links these two crazy things that seem totally unrelated) | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 239,501,588,589,182,980 | Ray | 01/30/2022 03:09:22 | integral of dy = y + C. do u understand how that's intuitive?
dy/dx = slope. do u understand how that's intuitive?
dy/dx * dx = dy. do u understand how that's intuitive?
integral of dy/dx * dx = y + C. do u understand how that's intuitive? | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:10:16 | how | 1 | 0 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:10:16 | Bro ok hold up | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:10:40 | @Ray the dy/dx * dx = dy thing always felt so hand wavy and sketchy to me | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:10:53 | When dy/dx is presented in calculus, it’s basically a symbol | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:11:05 | When did it become concrete values you can multiply by | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:11:28 | How? That’s what the proof explains | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:11:46 | they’re differentials? | 1 | 0 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:12:19 | the theorem says ‘if we have f, take the integral of it from a to x, then differentiate it, we get f back’ | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:12:37 | Exactly | 0 | 1 | 239,501,588,589,182,980 | Ray | 6714 | Ray | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:12:41 | how does it become | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 239,501,588,589,182,980 | Ray | 01/30/2022 03:12:44 | this is basically like doing u sub. it's hand wavy yes but it's legal b/c there is rigorous math behind it that lets u do that.
dy = dy * (dx/dx) = dy/dx * dx. this kinda thing u see in physics a lot | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:12:48 | How do you get f back? | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:12:50 | ‘integrals are opposite of derivatives’ | 1 | 0 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:13:12 | This doesn’t sound like opposites to you? | 0 | 1 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:13:31 | You take a function, integrate it up to x, differentiate with respect to x, and you get the original function back | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:13:32 | no | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:13:35 | They undo each other | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:13:52 | one you differentiate with respect to x | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:14:03 | one you integrate with respect to a and x | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:14:15 | Broooo I hate that a lot lol | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:14:21 | For applications I understand though | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 239,501,588,589,182,980 | Ray | 01/30/2022 03:14:28 | if u do A, and then do B, and doing B reverses when u did A isn't that opposites | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:14:34 | You can’t go through 10 hoops to avoid small logical problems | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:15:03 | It sounds like what you’re really asking is what these bounds are about | 0 | 1 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:15:23 | Would you still be confused if I said $$F(x) = \int f(t) dt$$ instead? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 510,789,298,321,096,700 | TeXit | 01/30/2022 03:15:25 | **abs\_0** | 307070375735459842.png | 0 | 1 | 239,501,588,589,182,980 | Ray | 6714 | Ray | false | ||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:15:26 | i guess? | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:15:43 | isn’t boundless integration introduced after ftc2? | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:15:53 | Yes, that’s precisely the issue | 0 | 1 | null | null | null | null | null |
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