The Yakubian Integral

∫₋∞∞ e⁻ˣ² dx Bro not this fucking useless integral ∫₋∞∞ e⁻ˣ² dx ∫₋∞∞ e⁻ʸ² dy And change it into a double integral ∫₀²π ∫₀∞ e⁻ʳ² ? dr dθ The new integrand the Jacobian, I mean Yakubian for polar coordinates is just r ∫₀²π ∫₀∞ e⁻ʳ² |Y| dr dθ My bad, Yakub u = −r² 2π ∫₋∞⁰ 1/2 eᵘ du Now we can do a substitution we know the integral is the ∫₋∞∞ e⁻ˣ² dx = √π. I’ve got a reward for you now…

A fast-paced educational meme explains how to evaluate the Gaussian integral by converting it into a double integral and then using polar coordinates. A stern illustrated figure introduces the problem, while a blond presenter walks through the calculation; the joke comes from repeatedly calling the Jacobian “Yakubian” and treating the solved integral as a reward, ending with an anime-styled character presenting it. Luude’s upbeat drum-and-bass version of “Down Under” featuring Colin Hay makes the mathematical explanation feel comically dramatic and energetic, turning a niche calculus pun into a rhythmic reveal.

♪ Luude — Down Under (feat. Colin Hay)

• @eternalclassic / 80994 2025-12-28