this post was submitted on 14 Jul 2025
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Hum... I don't think the integral "operator" applies by multiplication.
You can put the dx at the beginning of the integral, but not before it.
If you were using nonstandard analysis with dx an infinitesimal you could put it outside I guess. Maybe with differential forms too?
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.