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In my calculus II course we have to do a project where we apply integration to some aspect of our lives. We've learned a whole bunch of different applications of integration, including area, volume, work, averages, centroids, moments, arc length, surface area, laminar flow, cardiac output, probability, and also some of those applications applied to parametric and polar equations. Does anyone have any ideas on how I could somehow apply integration to the rubik's cube?

Also, I'm completely fine with learning a few more advanced topics such as matrix theory if that means a better project.

Also, I'm completely fine with learning a few more advanced topics such as matrix theory if that means a better project.