Brainee Posted May 31, 2023 Share Posted May 31, 2023 what doe f(x)dx mean and how is it used? Link to comment Share on other sites More sharing options...
swansont Posted May 31, 2023 Share Posted May 31, 2023 6 minutes ago, Brainee said: what doe f(x)dx mean and how is it used? f(x) represents a function of x dx is a differential; it’s found in an integral (you could integrate f(x)dx) or as a derivative, as in dy/dx Link to comment Share on other sites More sharing options...
Brainee Posted May 31, 2023 Author Share Posted May 31, 2023 in integrals? Link to comment Share on other sites More sharing options...
swansont Posted May 31, 2023 Share Posted May 31, 2023 2 minutes ago, Brainee said: in integrals? It’s calculus. https://en.m.wikipedia.org/wiki/Calculus Link to comment Share on other sites More sharing options...
exchemist Posted May 31, 2023 Share Posted May 31, 2023 (edited) 30 minutes ago, Brainee said: what doe f(x)dx mean and how is it used? I find the graphical representation of this the most helpful in understanding it. If you plot f(x) against x as a curve, f(x)dx - i.e. f(x) times the infinitesimal length dx along the x axis - is an infinitesimally thin vertical strip of area under the curve at the value x. If you add up a series of such strips you get a block of area under the curve. That is what integration does: it gives you the area under the curve representing the function, between two points on the x axis. The integral sign, ∫ , indicates a sum of these infinitely thin strips, adding up to a finite value for the area. Here is one example: https://www.bbc.co.uk/bitesize/guides/zq3ggk7/revision/1 This basic idea spins off into a host of applications, all over natural science and engineering. Edited May 31, 2023 by exchemist Link to comment Share on other sites More sharing options...
Brainee Posted May 31, 2023 Author Share Posted May 31, 2023 How do you calculate f(x) times dx? Link to comment Share on other sites More sharing options...
Genady Posted May 31, 2023 Share Posted May 31, 2023 Just now, Brainee said: How do you calculate f(x) times dx? You do not calculate it. It is not a number. Link to comment Share on other sites More sharing options...
Brainee Posted May 31, 2023 Author Share Posted May 31, 2023 Then what is it? Link to comment Share on other sites More sharing options...
Genady Posted May 31, 2023 Share Posted May 31, 2023 It is an expression which has a meaning as a part of something, e.g., of an integral. Link to comment Share on other sites More sharing options...
exchemist Posted May 31, 2023 Share Posted May 31, 2023 14 minutes ago, Brainee said: How do you calculate f(x) times dx? What you calculate is the integral. Have you looked at the example I gave you a link for? That shows you how you do the calculation. Link to comment Share on other sites More sharing options...
Genady Posted May 31, 2023 Share Posted May 31, 2023 If you understand what is dx, then dx is just f(x)dx in the case when f(x)=1. Link to comment Share on other sites More sharing options...
wtf Posted May 31, 2023 Share Posted May 31, 2023 (edited) 1 hour ago, Brainee said: what doe f(x)dx mean and how is it used? Some good news and some bad news. The good news is that [math]f(x) \rm{dx}[/math] has a completely rigorous mathematical meaning. The bad news is that it's an advanced topic in the undergrad or early grad school math curriculum, and basically not accessible to calculus students. I wish there were a better way. Differential forms are basically "things that can be integrated over suitable regions," but that doesn't really help us understand them. https://en.wikipedia.org/wiki/Differential_form Edited May 31, 2023 by wtf Link to comment Share on other sites More sharing options...
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