An integral that is out of this world!!

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Опубликовано:

9 июл 2024

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Комментарии : 22

@TheLowstef 17 дней назад

There's a mistake at the bottom of the left half of the final board. The second nested "e to the e to the..." only contains one "e to the..."

@henrymarkson3758 17 дней назад

Well done on reaching the 300K subscriber milestone. Thoroughly deserved.

@srr5v 17 дней назад

You were very patient for this one. Looking forward to your new videos (though most of the time for most of them I can't understand). Still enjoy your teaching videos though, thank you for the channel.

@demenion3521 17 дней назад

at 7:10 i would've written that as a complex contour integral along a semi-circle and used some residue integration to finish it off

@ekadria-bo4962 17 дней назад

How?

@aadfg0 17 дней назад

@@ekadria-bo4962 You can't unless there's a way of adding in a isin(θ) term. If you somehow introduce this term, integrand becomes e^(e^(iθ)) e^(iθ) dθ = -i e^z dz where z = e^(iθ), so you're integrating along upper semicircle. After that it's easy to find the value. But that's a big IF.

@Shindashi 17 дней назад

Damn this was beautiful.

@florisv559 17 дней назад

pi over 4 is a somewhat disappointing result for an out of this world integral. ;)

@user-gs6lp9ko1c 17 дней назад

I would have first solved it numerically, and (probably) would have recognized the decimal equivalent of pi/4. Having that, I would have a much better chance of finding the correct answer by solving analytically. 🙂

@s1nd3rr0z3 17 дней назад

Spoilers!!!

@emanuellandeholm5657 17 дней назад

So it kinda turns into a Fourier series type cosine transform, summed over the factorial of the wave number. That was not obvious to me from the get.

@VideoFusco 17 дней назад

You can rewrite cos teta with Euler's formula and solve the two integral in a very elementary way.

@davidcroft95 15 дней назад

The integral at 8:32 can be easily solved if you remember that cos(n*x) is a complete set of orthonormal functions and view the integral as an extention of the dot product: therefore it's always zero unless the input of the cosine functions are equal, in this case when n=1

@holyshit922 17 дней назад

Answer = π/4 I tried Gauss-Legendre quadratures for 20 nodes and error was quite large

@goodplacetostop2973 17 дней назад

11:18

@whiteboar3232 17 дней назад

Wow!

@user-vx1kd6ks3s 17 дней назад

Can I suggest a bit larger hand writing on the black board? It would make it more pleasant to follow without having to constantly guess, what is being written. Thank you! And thank you for sharing this incredible result!