MIT 2023 Quarterfinals #2-1

[@doronezri1043]

Excellent video👏👏👏 I liked completing the square, and at 02:51 we're kind of lucky🍻

[@owl3math]

thanks! :) 🍻

[@slavinojunepri7648]

Excellent

[@owl3math]

thanks Slavino!

[@FreeDom-tn3ce]

Nice integral

[@owl3math]

Thanks! 🙏👍

[@maxvangulik1988]

u=ln(x)
dx=e^u•du
I=int[1/2,♾️](e^(u-u^2))du
I=e^(1/4)•int[1/2,♾️](e^-(u-1/2)^2)du
t=u-1/2
dt=du
I=e^(1/4)•int[0,♾️](e^-t^2)dt
I=sqrt(pi•sqrt(e))/2

[@owl3math]

Thanks Max! 👍👍👍

[@Leonhardeuler2219]

Why did I meet you before? 🎉🎉🎉🎉

[@ChimezieFredAnaekwe]

Thanks for the video.
What is the intuition behind gaussian integral, and at stage in the university is one expected to know about it?

[@owl3math]

I don't believe it's taught in Calc 2 or any of the early Calculus classes. I think it comes up in advanced statistics because of the relationship to the normal distribution. It has many applications. This might be helpful: en.wikipedia.org/wiki/Gaussian_integral

[@ChimezieFredAnaekwe]

@owl3math Thanks for this information.

[@FreeDom-tn3ce]

It's like one I saw before:
∫ [e,∞] x^(1-lnx)

[@owl3math]

Oh yeah. Seems like the same idea