Finding Exact Area Under a Curve Using the Limit Approximation Method | Riemann Sums Explained
Автор: Math and Engineering Made Easy
Загружено: 2026-01-23
Просмотров: 3
Описание:
In this lecture, we explore how to find the exact area under a curve using the limit approximation method, the fundamental idea behind definite integrals.
Starting from Riemann sums and common numerical approximations (left sums, right sums, trapezoidal rule, Simpson’s rule), we take the limit as the number of rectangles approaches infinity to obtain the exact value of the area.
Using a detailed example with a quadratic function, we:
Construct the limit definition of area
Express the sum using Δx and sample points
Evaluate the resulting summation formulas
Take the limit as 𝑛→∞
Verify the result using definite integration
This lesson bridges algebra, limits, and calculus, helping you understand why integration works—not just how to apply formulas.
📌 Topics covered:
Riemann sums
Limit approximation method
Exact vs approximate area
Definite integrals
Area under a curve
💬 If you have questions or would like to see more examples, leave a comment below!
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#DefiniteIntegrals
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#LimitDefinition
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