The discussion clarifies the role of "dx" in integration, particularly in the context of integration by parts. "dx" represents the differential of the variable x, indicating the variable with respect to which integration occurs. It is distinct from "du," which is the differential of u, and omitting "dx" can lead to errors in more complex integrals, especially those involving trigonometric substitutions. Understanding these distinctions is crucial for accurate integration.
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Mostly it indicates the variable with respect to which you're integrating. It also is suggestive of the Δx in a Riemann sum.A.J.710 said:I'm doing integration by parts and I am a bit confused as to what exactly dx is.
That's not a good thing to do. dx doesn't play much of a role for very simple integrals such as substitutions. However, in integration by parts of trig substitutions, if you omit it, you will run into problems.A.J.710 said:Usually when integrating it is just dropped or forgotten about.
No, du is the differential of u. That's not the same as the derivative.A.J.710 said:Now when doing integration by parts there are some problems where you pick x as your u and dx as your du. since du is the derivative of u
I doubt that's what you were taught. "du of x" makes no sense.A.J.710 said:why isn't the du of x just 1 like we were always taught?
A.J.710 said:Why is it now dx?