Using Riemann Sums to Introduce Integral Calculus

With the “Mathematics” section of Decoded Science seemingly devoid of other contributors, I had decided to write a series introducing calculus. The obvious advantage of writing a series is the greater ease of deciding on topics.

Integral Calculus and Riemann Sums

Starting Integral Calculus by the Summation of Riemann Integrals” was published yesterday.

"Parabola Showing Approximate Area Under the Curve" by Mike DeHaan
“Parabola Showing Approximate Area Under the Curve” by Mike DeHaan

Integral calculus allows one to calculate the area under a curve. Often this represents the accumulated total produced by working at the rate pictured by that curve. An easy example is “How far did we drive, considering how long and how fast we were going”?

Bernhard Riemann developed the “Riemann Sums” along the way to formalizing integral calculus. My article explains how this process is an important step to understanding integral calculus.
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As always, I also promoted my Decoded Science article in my DeHaan Blog of Writing. The blog entry “Preview of Riemann Integrals” is actually a preview of the images I created to illustrate the main article, but also has more of my hopefully-popular writing tips.

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