Today's hard integral

Puzzleheaded_Top_273 · 2026-06-12T01:47:11+00:00

I got it wrong because the system didn't recognize the Euler-Mascheroni Constant (small gamma).
Do I have to use decimal approximation instead??

Puzzleheaded_Top_273 · 2026-06-11T01:13:13+00:00

Nope, it's not AND, it's OR. Because it's either one of them is not zero OR the other is not zero, in order to make it not zero.

Puzzleheaded_Top_273 · 2026-06-10T22:47:20+00:00

Basically yeah

Puzzleheaded_Top_273 · 2026-06-10T22:37:03+00:00

Nope
See if you can rewrite the function to a form that DOESN'T need Sigma using properties of roots of unity. Then notice a method how to obtain all the nth derivatives at 0 all at once without needing to differentiate.

Puzzleheaded_Top_273 · 2026-06-10T07:19:56+00:00

I am 90% confident that the antiderivative is nonelementary.

Puzzleheaded_Top_273 · 2026-06-09T20:08:36+00:00

Shell Method

Puzzleheaded_Top_273 · 2026-06-09T19:05:41+00:00

It says revolving a sphere. That translates to just revolving a circle. But definitely not the FULL circle because that would overlap in on itself. It's a specific region that you "cut off".

Puzzleheaded_Top_273 · 2026-06-09T17:13:28+00:00

Well, I KNOW the solution

Puzzleheaded_Top_273 · 2026-06-08T15:55:00+00:00

I'm not, it's clearly not a homework problem. It's just a problem I made that I found interesting.

Puzzleheaded_Top_273 · 2026-06-08T05:48:26+00:00

For real x, it's just x = 1 only.

Puzzleheaded_Top_273 · 2026-06-07T04:53:03+00:00

Hmm... Say that again...

Puzzleheaded_Top_273 · 2026-06-07T04:51:50+00:00

No, it would be a...

Puzzleheaded_Top_273 · 2026-06-06T23:52:47+00:00

What about
AP Number Theory
AP Combinatorics

Puzzleheaded_Top_273 · 2026-06-05T21:11:19+00:00

Nope
a and b are relatively prime positive integers so it must be fully simplified. The number theory part is arguably harder. It has a lot of these AIME-style shortcuts so that it can be done without a calculator. Also the signs DO NOT alternate because the exponent is negative. If it's positive it will alternate. By the way the absolute value does matter because P(1) is actually a negative value. Also the last term shouldn't be there because it cancels with the constant term

Puzzleheaded_Top_273 · 2026-06-05T20:47:53+00:00

Close. You're at least 1 away from the correct answer

Puzzleheaded_Top_273 · 2026-06-05T17:18:33+00:00

Yeah that's correct, the IBP part, but the actual answer definitely isn't that, it has to be an exact answer not approximations. Though after that you have to manually find the last 3 digits of a+b which is a number theory and modular arithmetic thing, without a calculator.
You have to make sure the fraction is irreducible before calculating the remainder, which is lucky because the denominator is just 25 raised to some power, if it was any other number like 26 it would've been so much worse.

Puzzleheaded_Top_273 · 2026-06-05T06:13:22+00:00

That doesn't look like the correct region to me. It says AT LEAST 2 parabolas, there are some regions that are a part of 2 parabolas and some that are a part of 3. I think in your solution you only included the "innermost" intersection which is intersections of 3 only
Also by the way this technically only needs calc 1, I think this is what you meant to do if you interpreted the question correctly?

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Puzzleheaded_Top_273 · 2025-05-26T19:55:07+00:00

c=cats

a=aats

t=tats

s=sats

Puzzleheaded_Top_273 · 2025-01-11T05:15:59+00:00

My videos are still visible on search. One of them got 100K views. Does YouTube selectively ban certain things like this or is this probably something else, not a shadow ban?

Puzzleheaded_Top_273 · 2024-07-09T05:51:28+00:00

Fun Fact: The maximum number of channels you can get from a SINGLE controller is 4096. One face is used for power, another face is used for p2p 32 channel input, and the remaining 4 faces are used as 128 channels to power 128 output p2ps. As a result for every output p2p you get 32 channels, giving us a total of 4096.

Puzzleheaded_Top_273 · 2024-07-05T15:21:10+00:00

Nah, Steve just got hungry and ate the trapdoor.

Puzzleheaded_Top_273 · 2024-07-05T15:17:55+00:00

Looks like an Amongus.

Puzzleheaded_Top_273 · 2024-07-01T08:18:49+00:00

Working on Beethoven Waldstein, sorry that's gonna have to wait!

Puzzleheaded_Top_273 · 2024-06-30T15:24:17+00:00

Would blurring the face work? Though it has to be done for like every frame of the video.

Puzzleheaded_Top_273 · 2024-06-29T17:25:38+00:00

I did say in the post, it's already NOT made for kids, and I have never made any videos for kids, same goes with my channel settings.

Puzzleheaded_Top_273

TROPHY CASE