Approximating Area Under a Curve with Rectangles
Approximating Area Under a Curve with Rectangles
May 10, 2020
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@gamma.mathematica on Instagram: "Riemann sums and integrals both aim to calculate the area under a curve, but they differ in precision and method. A Riemann sum is an approximation, where the area is estimated by summing the areas of rectangles under the curve. The width of each rectangle is based on a partition of the interval, and the height is taken from the function’s value at a chosen point within each subinterval (like the left endpoint, right endpoint, or midpoint). As the number of rect
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@gamma.mathematica on Instagram: "Riemann sums and in…
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Soufiane Lad on Instagram: "🔥 Why 1/2 + 1/3 + 1/4 + ... = INFINITY? 🤯 Ever wondered why adding smaller and smaller fractions can still blow up to infinity? 🚀 In this video, I prove that the harmonic series DIVERGES using the integral test! 📊 The Key Idea: ✨ Each term 1/n forms a rectangle ✨ The sum of rectangles > area under the curve y = 1/x ✨ ∫(1/x)dx from 1 to n = ln(n) ✨ As n → ∞, ln(n) → ∞ ✨ Therefore, the harmonic series = ∞! This beautiful proof connects calculus and infinite series i
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Soufiane Lad on Instagram: "🔥 Why 1/2 + 1/3 + 1/4 + ... = INFINITY? 🤯 Ev…
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