Accumulation functions

Introduction to the idea of creating a new function from an old function by means of definite integration. This new function measures "accumulated area" under the graph of the original function. When the original function represents rate of change of some quantity, then the accumulation function represents net change in that quantity. Two examples are examined. The video also discusses the idea of "helper variables", auxiliary variables that show up in, for example, summation, integration, or limit evaluation, whose "names" are irrelevant to the process.
ERRATE and COMMENTARY
• At 1:58 and a bit later I wrote "3-1/3" when I meant "9-1/3". Fortunately, the final answer "26/3" is correct. (Thanks to Mark Lavigueur for pointing this out.)

[@AndyZengtheGreat]

Dr. Odden always makes the best videos to help us dying 590 students survive

[@huyhangtran4315]

This was a well-done video. You've been helping to progress teaching math with some of the software/presentation techniques you have here. It helps to provide subtle animation or more visual representation of difficult concepts for students than ever before. Keep going, others need exposure to your material so the teaching world will progress in explaining concepts more clearly and with more resources at their disposal to make the learning even more accessible to different types of learners.

[@huyhangtran4315]

And awesome, awesome, AWESOME job on providing a substantial "note" in the first half of this video; I see this is your solution to provide some helpful "tips" or commonly misunderstood prerequisite knowledge that is needed to understand newer content (in this case; accumulation functions).

[@chrisodden]

Thanks so much for the thoughtful comments. I try to cover subtle but important points I think often get missed, so it is gratifying to read your observation. I also feel strongly that if one takes the trouble of creating a video, then it is worth using the kinds of effects that video makes possible!

[@sankalps.9775]

Thanks so much!

[@punditgi]

Keep those videos coming! I love 'em!

[@punditgi]

Nice video, Chris!
Why say "helper variable" instead of "dummy variable"?
Also, why not use metric in your examples? All other countries outside the USA (including Canada, UK, Australia, etc.) use it and so do we in physics problems.

[@chrisodden]

To be honest, Ezra, I thought it sounds nicer. :)

[@tasninnewaz6790]

@@chrisodden hahaha.... Really, It's comforting to say.

[@VishnuMurthy]

Awesome!

[@marklavigueur7157]

In the first example should be 9-1/3, no?

[@chrisodden]

Thanks for spotting this! I have added a note about this in the description.

[@anilsharma-ev2my]

Energy accumulation become what ???