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MATHEMATICAL BEAUTY

Integration as the Limit of a Riemann Sum

Explore how the area under a curve can be approximated using rectangles — and watch the approximation converge towards the exact integral.

Rectangles
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Riemann Sum

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Exact Integral

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The blue rectangles use the left endpoint of each interval to estimate the area beneath the curve. As the number of rectangles increases, their width becomes smaller and the Riemann sum approaches the exact integral. In the limit, this is the definition of integration.

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