Wow! This is a VERY instructionally valuable way of presenting this! Did you come up with it? Or, did you read it in a book somewhere - because in that case, I'd love to see that book! Regardless of which is the case, thank you for making a video on it! +1
Thank you for this explanation! One question: what about the y-axis? How not to confuse it with the u-axis (because they are in the same plane in this video)?
It's because I've drawn it flat. You could have drawn it like a 3D system, and the y axis would be vertical. You could just make a y axis here vertically and then another copy of it horizontally .
Great. Would be nice to include the examples when the function u is not a biyective function and is possible for one u to be the image of more than one x, and also when in the integration, there is a factor x that is left over and has to be changed in terms of u
That's a good idea. For the latter part, we could do it by drawing tiny slope triangles along the connecting curve, and showing how the slope changes along the curve u. I actually sketched this out some years ago but never got around to making a video of it.
Thanks for doing what the university teachers refused to. I wonder how awful the visual representation gets once you substitute something that is polynomial or even periodical
