f(x)dx

[Brainee]

what doe f(x)dx mean and how is it used?

[swansont]

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

[Brainee]

in integrals?

[swansont]

2 minutes ago, Brainee said:

in integrals?

It’s calculus.

https://en.m.wikipedia.org/wiki/Calculus

[exchemist]

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

[Brainee]

How do you calculate f(x) times dx?

 

[Genady]

Just now, Brainee said:

How do you calculate f(x) times dx?

 

You do not calculate it. It is not a number.

[Brainee]

Then what is it?

[Genady]

It is an expression which has a meaning as a part of something, e.g., of an integral.

[exchemist]

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.

 

 

[Genady]

If you understand what is dx, then dx is just f(x)dx in the case when f(x)=1.

[wtf]

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