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I watched this video, and the only thing that confused me was the very start, where he placed the integration symbol as an infinite summation symbol. How can he do that? It feels very unrigorous and loose.
Basically, can anyone show/link me to a proof that shows that I could just put an indefinite integral symbol in front of a differential to add it all up?
I hope the proof isn't too complicated. I don't want this to be another "you can treat dy/dx as a fraction" without a clear reason why.
P.S. I went to the following definition of an integral:
But it wasn't helpful. Thank you in advance!
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