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

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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?
 

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  • #2
berkeman
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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
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What's a 2nd derivative and double integral?
 
  • #4
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Line said:
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.
 
  • #5
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
Hootenanny
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Gelsamel Epsilon said:
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 :wink:
 
  • #7
If you're asked for the general solution x³ is sufficient. :tongue2:
 
  • #8
HallsofIvy
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Hootenanny said:
''f = x3 +C :wink:
Actually, if f= 6x, then 'f= 3x2+ C so "f= x3+ Cx+ D.
I'm very puzzled by
Gelsamel Epsilon said:
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.
 
  • #9
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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
Ha, sorry HallsofIvy I confused myself, I meant if you're asked for "an" (rather then "the") antiderivative then that satisfies.
 
  • #11
HallsofIvy
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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.
 

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