Antiderivative

if our IQ is too low

All rational functions have an elementary anti derivative.

>>7017342
find the values where x3+x2+1=0, go complex, shift the zeroes by i \epsilon , find a contour which vanishes and use the residue theorem to inegrate.

All functions have an antiderivative, it is simply not always computable in terms of elementary functions

>>7017354
>All functions

no

>>7017359
why?

>>7017365
Please take a math class and learn what an integral is.

>>7017365
Weierstrass functions

>>7017354
If the function is absolutely continuous (on a compact interval), then there is an antiderivative. In any other cases, you can't know it.

>>7017371
You are retarded. The Weierstrass function is continuous, hence has an antiderivative.

>>7017365
Function has to be continuous.

>>7017378
Are you fucking retarded? Absolute continuity is a much stronger condition than continuity.

>>7017342
Try to break it down in simple elements.

>>7017382
>Are you fucking retarded?
Yes, I got confused with another property. Sorry.

File: A discontinuous Riemann integrablefunction with an antiderivative..jpg (43KB, 471x374px) Image search: [Google]

43KB, 471x374px

>>7017381

>>7017397
how about f(x)=1 of x=0, f(x)=0 for every other x

this can't be the derivative of any g(x), because then f should assume every value between 0 and 1

>>7017354
>>7017359
>>7017365
>>7017367
>>7017371
>>7017378
>>7017380
>>7017381
>>7017382
>>7017397

If g is a Lebesgue-integrable function on some interval [a,b] and we define f as:

f(x) = \int_a^x g(t)dt

then:

1. f is absolutely continuous
2. f is differentiable almost everywhere
6. it's derivative coincides almost everywhere with g(x)

So, if g is Lebesgue-integrable then, almost everywhere, f' = g (i.e it has an antiderivative).

>>7017401
Your function f is a weak derivative of every constant function.

>>7017406
so?
why does that imply if f is a weak derivative of some g than there is a h such that f is the strong derivative of h?

we were looking for functions that dont have antiderivative

>>7017405
>almost everywhere

File: 7-9.jpg (89KB, 453x507px) Image search: [Google]

89KB, 453x507px

>>7017397