Can you give me an example of a bounded f:[0,1]-> R , which has a primitive but it isn't Riemann-integrable? It must be on a closed interval from zero to one.
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Here's a MathJax tutorial :) – Shaun Feb 28 '18 at 19:51
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Suositeltua lukemistoa kysymisestä yleensä ja MathJaxin käytöstä (LaTeXin mark-up versio) – Jyrki Lahtonen Feb 28 '18 at 19:55
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2Can you give a definition of has a primitive, please? I thought that a primitive of $f$ is a differentiable function $F$ with derivative $F'=f$. Is the idea that we only require that almost everywhere? Or what? Sorry about being rusty here, this may be a standard definition :-) – Jyrki Lahtonen Feb 28 '18 at 19:58
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Can you provide some contexts? Depending on the restriction (such as boundedness on the derivative) a counter example can be quite involved. – Sangchul Lee Feb 28 '18 at 20:03
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Hey, In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F ′ = f. – Sanderi Feb 28 '18 at 20:11
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I have tried x^2sin(1/x) and 1/x. It must be bounded in the closed interval [0,1] – Sanderi Feb 28 '18 at 20:13
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It has to have a primitive but no Riemann-integrable. Sorry for bad English. – Sanderi Feb 28 '18 at 20:17
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Thanks for help guys – Sanderi Feb 28 '18 at 20:22
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Anna esimerkki rajoitetusta funktiosta f : [0, 1] → R, jolla on primitiivi, mutta joka ei ole Riemann-integroituva. This is the question in Finnish. – Sanderi Feb 28 '18 at 20:31