# In Calculas I've learned that 'F means the integral of a function.

1. Aug 29, 2006

### Line

In Calculas I've learned that 'F means the integral of a function. SO what does ''F mean, th integral or an integral of a function?

2. Aug 29, 2006

### Staff: Mentor

I hadn't seen that notation before. I suppose it could be the analog of the shorthand notation for derivative?

f = function
f' = derivative of f
f'' = 2nd derivative of f
'f = integral of f
''f = double integral of f

3. Aug 29, 2006

### Line

What's a 2nd derivative and double integral?

4. Aug 29, 2006

### d_leet

You didn't learn much in calculus did you? A 2nd derivative is pretty much what it sounds like the derivative of a derivative, and sort of similar for a double integral.

5. Aug 29, 2006

### Gelsamel Epsilon

f = x³
f' = 3x²
f'' = 6x

f'' is just the derivative of f'.

Also, f, is the ''f (double intergral) of f'' so if f = 6x then ''f = x³. I hope that wasn't confusing.

6. Aug 30, 2006

### Hootenanny

Staff Emeritus
''f = x3 +C

7. Aug 30, 2006

### Gelsamel Epsilon

If you're asked for the general solution x³ is sufficient. :tongue2:

8. Aug 30, 2006

### HallsofIvy

Actually, if f= 6x, then 'f= 3x2+ C so "f= x3+ Cx+ D.
I'm very puzzled by
It is precisely when you are asked for the "general solution" that you must have the entire form! x3 does satisfy the conditions but is not the "general solution". Neither is x3+ C. The general function "f such that f= 6x is "f(x)= x3+ Cx+ D.

9. Aug 30, 2006

### JonF

When I was in calc and I took test the first thing I always did was write +C down the most the right side of the page.

10. Aug 30, 2006

### Gelsamel Epsilon

Ha, sorry HallsofIvy I confused myself, I meant if you're asked for "an" (rather then "the") antiderivative then that satisfies.

11. Sep 1, 2006

### HallsofIvy

It is not uncommon to use the notation f(n) to mean the nth (notice the parentheses) rather than f', f", since it is clearer if n is large. Similarly, a common notation for "nth anti-derivative" is f(-n). I had never seen 'f, "f before.