Power rule of integrals not using integration; definition of e | DIw/oI #7

You know the power rule for integration, but can we derive the rule without integration? (What does this question even mean?) And can we have a visual definition of e? This video answers them all.

This should really be the last video in the series of Doing Integrals without Integration, unless there are other ideas that fall into the umbrella of calculating some (curved) areas without integration.

This idea was originally from Fermat, right before the invention of calculus. I cannot find any easy-to-read literature / source on the exact same topic, so if you happen to find one, please let me know in the comments.

This whole video is adapted from a book called e: The Story of a Number by Eli Maor, which is a very good recreational mathematics book that I recommend all to read.

Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
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If you want to know more interesting Mathematics, stay tuned for the next video!

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#mathemaniac #math #integration #powerrule