Formula Guide for Students on Instagram: "This integral appears in probability, quantum mechanics, and heat equations. A true classic of mathematics — save it! 📐✨ #gaussintegral #calculus #advancedmath #studygram #mathlovers #brainfuelnotes #engineeringmaths"

Mathematisa | Math Animations on Instagram: "The Gaussian Integral: Why √π is Everywhere in Math & Science Have you ever wondered why the "bell curve" has such a mathematically perfect area? Let's unpack one of the most elegant results in all of mathematics: ∫₋∞ᴵᴺᶠ e⁻ˣ² dx = √π. It seems impossible at first—how can this beautifully smooth curve, fading to zero at both ends, have an area exactly equal to the square root of π? The function e⁻ˣ² has no elementary antiderivative (thank the Risch alg