What is the correct notation for integrating F(x)?

  • Thread starter majin_andrew
  • Start date
  • Tags
    Integrating
In summary, the conversation discusses the correct notation for the integral of a function F(x) and whether there is a standard notation for it. The conclusion is that there is no standard notation, with some suggestions for possible notations in certain cases.
  • #1
majin_andrew
20
0
Hi, this isn't a homework question, I'm just curious about this.

I am wondering what the correct notation is for the integral of F(x).

For example,
integral of f''(x) = f'(x) + c
integral of f'(x) = f(x) + d
integral of f(x) = F(x) + e
integral of F(x) = ??

I feel silly for not knowing this. Is there a common notation that I am not aware of, or is it simply a case of letting F(x) = g''(x) (or whatever) and carrying on from there?

Thanks!
Andrew
 
Physics news on Phys.org
  • #2
There isn't any standard notation for that. Even integral f(x)=F(x)+C isn't really standard. It's common to write that when you are being introduced to antiderivatives, but in general if you write 'F(x)' you should never assume someone will automatically know it's the integral of f(x).
 
  • #3
Edit: Sorry had trouble with the equation editing
 
  • #4
Okay thanks for that Dick. So if I would like to write the second integral of f(x), is it the proper notation to write it as [tex]\int{\int{f(x)d^2 x^2}[/tex] ?
 
  • #5
majin_andrew said:
Okay thanks for that Dick. So if I would like to write the second integral of f(x), is it the proper notation to write it as [tex]\int{\int{f(x)d^2 x^2}[/tex] ?

Even the first integral should really be written [tex]F(x)=\int_a^x f(t)dt[/tex]. The x dependence is really in the limit not in the dummy integration variable. [tex]\int f(x) dx[/tex] is really pretty casual. And you are REALLY stretching the definition of casual with that notation. Seriously, you very seldom need a 'second antiderivative' of f(x). That's probably why there is no good notation. If you do need it then just write 'pick g(x) to be a function such that g''(x)=f(x)'. Something like that.
 
  • #6
Ok, thanks for your help.
 
  • #7
Although there are few cases where it is needed, the Jn notation is used frequently in texts on integral equations and D-n in texts on fractional calculus, each for repeated integration.
 

FAQ: What is the correct notation for integrating F(x)?

What is "Integrating further than F(x)"?

"Integrating further than F(x)" refers to the process of taking the integral of a function multiple times, resulting in a nested integral. This is also known as repeated integration.

Why would someone integrate further than F(x)?

Integrating further than F(x) may be necessary in certain mathematical or scientific problems that involve multiple variables or complex functions. It can also be used to solve differential equations or to find the area under a curve.

What are the steps for integrating further than F(x)?

The steps for integrating further than F(x) are the same as regular integration, with the additional step of integrating the resulting integral again. These steps include finding the antiderivative, applying the limits of integration, and evaluating the integral.

Can integrating further than F(x) be done with any type of function?

Yes, integrating further than F(x) can be done with any type of function as long as it is continuous and differentiable within the given limits of integration.

What are some applications of integrating further than F(x)?

Integrating further than F(x) has various applications in mathematics, physics, and engineering. It can be used to solve problems in areas such as mechanics, thermodynamics, and electromagnetism. It is also commonly used in fields such as economics, biology, and chemistry to model and analyze complex systems.

Similar threads

Replies
4
Views
848
Replies
9
Views
1K
Replies
1
Views
647
Replies
1
Views
1K
Replies
3
Views
1K
Replies
9
Views
1K
Replies
15
Views
2K
Back
Top