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I'm taking integral calculus at the moment. I was understanding everything quite well until we started learning about finding volume of a solid of revolution. I understand the concept, but practicing it has been stressful to say the least.

I think if there was an app that takes a function and its boundaries, to then rotate about some axis for me then I would have a much better time understanding how to inspect what things like inner/outer radius, height, etc might be. Plus, I'd like to have very nice image examples to import into my digital notes so that I can review my notes and get a much better grasp of what's happening.

Is there any such tool I could use?

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  • $\begingroup$ Most computer algebra systems can do this. For example, see Sage's documentation doc.sagemath.org/html/en/reference/plot3d/sage/plot/plot3d/… $\endgroup$
    – Adam
    May 24, 2020 at 14:34
  • $\begingroup$ Not what you asked for, but the detailed definite integral set-ups I posted for my students and others back on 23 February 2003 might be of use, maybe for practice purposes. $\endgroup$ May 24, 2020 at 17:00
  • $\begingroup$ @DaveLRenfro That might help me out. I can integrate without a problem, but it's the setup for applications I struggle with. I'll check that out soon $\endgroup$
    – Lex_i
    May 24, 2020 at 17:44
  • $\begingroup$ If you're interested, I can send you a .pdf of one of these (or one that is very similar; I'm not sure if it's exactly the same as one of those) worked out with 2-dimensional sketches that I would use in class to show how to set up the integrals. You can find my email address here. $\endgroup$ May 24, 2020 at 18:53

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I suggest Geogebra. There are some great conceptual activities there that will help you with volume. My favorite creator is Tim Brezezinski. The following link will take you to an activity that does what you want:

https://www.geogebra.org/m/YpqytNph#material/BZWTCPfd

For a wider range of activities that look at volume of many kinds in depth you can go to https://www.geogebra.org/m/YpqytNph#chapter/163298 which is part of his Geogebra calculus "book"

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You seem like a real go getter, so I would suggest learning a real language that will generate some nice graphs and is going to come in handy down the line. Maybe try Python?

I made you a little starter notebook for solids of revolution here:

https://colab.research.google.com/drive/19hdZziUxA3RoXg0OEG2ktX1elQWQrfZW

You should get an idea of how to generate a 3d plot with Python here.

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