Godamn internets, FFS FFToC & SFToC. (1 Viewer)

[Forbidden.]

Wikipedia's definition of the FFToC (First Fundamental Theorem of Calculus)
http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for all x in [a, b], by

Then, F is differentiable on [a, b], and for every x in [a, b],

The operation

, dt is a definite integral with variable upper limit, and its result F(x) is one of the infinitely many antiderivatives of f.


Wikipedia's definition of the SFToC (Second Fundamental Theorem of Calculus)
http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be an antiderivative of f, that is one of the infinitely many functions such that, for all x in [a, b],

Then

.



Mathworld's definition of the FFToC (First Fundamental Theorem of Calculus)
http://mathworld.wolfram.com/FirstFundamentalTheoremofCalculus.html

The first fundamental theorem of calculus states that, if f is continuous on the closed interval [a,b] and F is the antiderivative (indefinite integral) of f on [a,b], then

.


Mathworld's definition of the SFToC (Second Fundamental Theorem of Calculus)
http://mathworld.wolfram.com/SecondFundamentalTheoremofCalculus.html

The second fundamental theorem of calculus holds for f a continuous function on an open interval I and a any point in I, and states that if F is defined by the integral (antiderivative)

then

at each point in I, where F'(x) is the derivative of F(x).

 

[Trajan]

Fark we has so little time to exam

hahaha, exams started today for me...

yeah we have very very little time til exams.

 

[darkliight]

Wikipedia's definition of the FFToC (First Fundamental Theorem of Calculus)
http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for all x in [a, b], by

Then, F is differentiable on [a, b], and for every x in [a, b],

The operation

, dt is a definite integral with variable upper limit, and its result F(x) is one of the infinitely many antiderivatives of f.

Ugh, that was wrong almost everywhere. Fixed the article -- hopefully not too late!