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Thank you!

I'm afraid I do not understand the question. Could you please clarify?

@@ConceptualCalculus Simply stated I would think the graph of the problem would have an X and a Y coordinate. The reason being most antiderivatives shoùld be able to be solved by finite element analysis.

@@Black_Cats_Of_War You could make a graph with position on the horizontal and weight on the vertical. In that case the position (which I called y) would be your x, and the weight remaining to be lifted would be your y. I'm not sure why you would bring in finite-element analysis when this is such a simple integral.

You could do it faster if you had formulas for the functions, or if you had lists of coordinates of the points. If all you have are the graphs, I don't know of a faster way. This is not intended to be done often. We add a few functions this way to get the concept, and then use that concept to do other things.

Thank you! I'm glad I could help.

Thank you. My channel is very small (about 300 subscribers right now) so it does not make the top of the search results when people are looking for math vids. Also, this vid does not directly address the all-important question "How can I get the right answer on my homework that is due in an hour?" I'm working on the first problem. No clues what to do about the second. I've learned a lot more about how to make videos since I made this one. Sometimes I think I should re-do it, but I haven't found the time yet. Check out some of my newer vids. They have better production values and more immediate relevance to homework that is due next week. Still nothing that cuts directly to the answer for homework that is due in an hour, though. ;-)

Thank you!

I can't recall ever seeing that notation used. If sin^-2(x) means anything I think it would have to be 1/(sin(x)^2). I can't imagine using it to mean (arcsin x)^2.

@@ConceptualCalculus alright, thanks!

I'm glad it was helpful.

You are right about that. As long as you stick with this simple problem structure, the answer is always that the work is equal to the weight multiplied by the distance moved by the middle of the chain. I didn't want to offer that as a short-cut to the answer, though, because the point of these problems is to learn the method, which also applies to much more complicated problems that don't have such simple answers. We're warming up to emptying odd-shaped tanks, and that kind of thing. I was afraid that if I offered a quick route to the exact answer then no one would pay any attention to the method. They would score a few easy points today and fail something larger later. Glad you liked the vid. I hope to make more this summer.

It always represents an inverse--depending on how you are using the word inverse. A number to the power -1 is the *multiplicative* inverse of the original number. That is, if you multiply a number by itself to the power -1, you always get 1 (unless your number is 0, which does not have a multiplicative inverse). Multiplicative inverse is not the same as function inverse, of course, but both represent a process that exactly reverses the original process. I don't know much about the history of math. At a guess, I would say they were building off of the idea of a multiplicative inverse, and using symbols readily available on a typewriter keyboard.

@@ConceptualCalculus thank you for elaborating on that.

@@JoshuaJohnsonOutdoors You're welcome. Happy to help.

Glad I could help.

You are welcome. I hope you also watched the Houston Math Prep. They explain the ideas behind what we are doing on Excel. It is good to know both the how and the why.

@@ConceptualCalculus Thank you!! The class day i missed was basically lab day so this video covered the lab portion of what i missed.

When you copy that cell down to all the cells below it, you want it to keep using the value of h that is stored in E1. You don't want it to use E2, E3, E4, etc.

You're welcome! I'm glad it was useful to someone.

@@ConceptualCalculus *some people* including me 😃

Thank you!

Thank you!

Thank you!

You think science doesn't have any annoying notation?

I'm glad to be able to help.

Thank you!

Thank you.

Thank you!

Thank you. The next vid will take a while. I have another project I have to finish first.

Thank you.

Thank you!

Math good. Notation annoying.

Thank you.

Thank you.

Thank you. I'm glad it was useful. I'm going to do arc length next.

Hey, Doug. This is actually about an application of integration. Integration is sort of the derivative done backwards. I don't have any vids on derivatives yet. I may do that after I finish this project, but I have a lot more to do here first. The series on applications of integration will probably end up with 15 to 20 vids when it is done.

Thank you.

Glad it was helpful!

Thank you.

You're welcome 😊

I'm happy that you see it that way. I think the Fundamental Theorem of Calculus is amazing. Of course, a lot of beginning students think the meaning of the derivative is to bring down the exponent and subtract one, which can be a bit tedious. When you really understand what it means, it becomes fascinating.

Thank you.

A viewer who is not a student in one of my classes? Yay!!! Thank you.

Thank you!