I'm going to write a paper focused on mathematics in the future and am still in the process of finding a captivating subject to explore. I believe that my greatest interest lies in calculus and have been considering different topic within it. One that caught my attention due to its comprehensibility was multiple integration.
However, I'm unable to find many intriguing uses for it. The two best ones I found was modelling radioactive decay and calculating total internal energy of a neutron star as in this paper: http://www.physics.drexel.edu/~bob/Term_Reports/Whitehead_hw1.pdf
And so I'd like to ask you for any interesting suggestions and ideas that you know of. They don't have to be physically focused as the ones I mentioned (although those are usually my favourites), any input is appreciated.
Thank you in advance.
just as a brief comment, here are some fundamental applications of multiple integrals that come to my mind:
1) in mechanics, the moment of inertia
2) Maxwell's equations written using multiple integrals to calculate the total magnetic and electric fields
3) Applications to Area, Volume, etc... (we do live in a 3D world :D)
4) Probability
Maybe you can consider the Spherical Cow metaphor, and thus talk about how multiple integration can be applied to all kinds of things?