The Riemann Sum

Riemann Sums are perhaps one of the most commonly taught of Riemann’s contributions. In any basic calculus class, it is quickly taught that taking the area of a curve is impossible to do unless infinite sums are involved. Riemann approximations take small rectangles that enclose minute amounts of the curve and sum them all together to get a close estimate to the area under that curve. However, when applied infinitely, each the widths of each rectangle will get infinitesimally smaller and approach zero – eventually leading to the mathematically exact area under the curve.

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