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?
The "dx" in an integral represents an infinitesimal change in the variable of integration, which is typically denoted as "x". It is used to indicate that the integral is being evaluated with respect to that specific variable.
"dx" is used in integrals to represent the tiny intervals or slices along the x-axis that are being summed up to find the total area under a curve. It helps to show that the integral is being evaluated with respect to the variable of integration.
Yes, "dx" can be replaced with any other letter or symbol to represent the variable of integration. This is commonly done when dealing with multi-variable integrals, where different variables are used for each integral.
No, "dx" is not a variable in itself. It is used as a notation to represent the variable of integration in an integral. It is important to understand that the integral is not just a sum of infinitely many "dx" terms, but rather a single quantity representing the total area under the curve.
"dx" and the derivative are closely related, as "dx" represents an infinitesimal change in the variable of integration, while the derivative represents the instantaneous rate of change of a function with respect to that same variable. In fact, the fundamental theorem of calculus states that the derivative and the integral are inverse operations of each other.