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

[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?

 

[berkeman]

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

 

[Line]

What's a 2nd derivative and double integral?

 

[d_leet]

What's a 2nd derivative and double integral?

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.

 

[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.

 

[Hootenanny]

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

''f = x³ +C

 

[Gelsamel Epsilon]

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

 

[HallsofIvy]

''f = x³ +C

Actually, if f= 6x, then 'f= 3x²+ C so "f= x³+ Cx+ D.
I'm very puzzled by

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

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.

 

[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.

 

[Gelsamel Epsilon]

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

 

[HallsofIvy]

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