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The bell curve: e^(-x²). It has NO elementary antiderivative — you literally cannot integrate it the normal way. Yet the total area under it is exactly √π. The trick: don't solve I. Solve I². I² = (∫e^-x² dx)(∫e^-y² dy) = ∬ e^-(x² y²) dx dy That's a double integral over the whole plane. And x² y² = r². Switch to polar coordinates. In polar form an extra r appears — and THAT r makes it integrable. Angle gives 2π. Radial gives ½. I² = 2π · ½ = π So I = √π. A flat integral, solved by lifting it int
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