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Matheorems on X: "Sum becomes integral. Top: the Riemann sum Σ f_i(x)Δx with Δx = x_m/N. Each time N doubles, every rectangle splits in two, and the total creeps up toward the exact area. Bottom: the exact area ∫₀^{x_m} f(x)dx under the same curve. Here f(x) = eˣ and x_m = 1, so the area is e − 1 = 1.71828… N = 1, 2, 4, … 1024: 1.00000 → 1.71744. As Δx → 0 and N → ∞, the sum becomes the integral." / X
3 days ago
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