this post was submitted on 14 Jul 2025
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If you were using nonstandard analysis with dx an infinitesimal you could put it outside I guess. Maybe with differential forms too?
In the context of differential forms, an integral expression isn't complete without an integral symbol and a differential form to be integrated.
Switch it with a summation operator and see if it makes sense. The problem isn't the operation by itself, but the fact that the operator implies an argument application, like a function.
In the case of dx as an infinitesimal it makes sense. You are making a sum of all the values of the function in the integral range and multiplying with a constant dx.