Preview of Riemann Integrals

I generally publish a preview of images I have created for other web sites. Here are my new images for my Decoded Science article, "Starting Integral Calculus by the Summation of Riemann Integrals".

"Parabola with Area Under the Curve" by Mike DeHaan

This picture was the building block for the later images of parabola.

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"Parabola Showing Exact Area Under the Curve" by Mike DeHaan

This parabola shows the "exact" area under the curve. On second thought, it should have been a green colour.

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

The same parabola shows 2 different approximations for the area under the curve.

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"Riemann Sum Formula" by Mike DeHaan

Riemann's formula for the sum of Riemann intervals is a masterpiece when copied from a Word document wherein the Greek "symbolic" alphabet can be used.

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"Integral Symbol" by Mike DeHaan

Here is my best attempt to draw the "integration function" symbol.

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Writing Tips

As always, I also promote my articles by mentioning them in my DeHaan Directory's "DeHaan Writing" page, as well as on DeHaan Services blog. The blog post is "Using Riemann Sums to Introduce Integral Calculus".

Writing Tips:

Obviously, I continue to lay claim to images by publishing them in "my own" blogs.

More important is the need to research carefully. I knew that I wanted to continue my series on calculus. The explanation for Riemann integrals was adapted from a fine textbook written at the university level. Let me be clear: the article is in my own words. However, I owe a lot to the professor for laying out the structure and logical flow. (I did change the order of a couple of items). This research gave me the logical sequence necessary to carry the discussion forward.