Question Number 203875 by MathedUp last updated on 31/Jan/24
![Hmmm..... I have one Question. f(t)∈C^∞ , {C_ ^𝛂 mean can derivate 𝛂 times.} where t∈R , Can f(t) integrable when S∈R\{Q}?? Ex. integral ∫_1 ^( e) ln(z)dz S∈[1,e] But Except Q in set S like.. S^′ =S\{Q} than Can integrable In S′](https://www.tinkutara.com/question/Q203875.png)
$$\mathrm{Hmmm}…..\:\mathrm{I}\:\mathrm{have}\:\mathrm{one}\:\mathrm{Question}. \\ $$$${f}\left({t}\right)\in{C}^{\infty} \:,\:\left\{{C}_{\:} ^{\boldsymbol{\alpha}} \:\mathrm{mean}\:\mathrm{can}\:\mathrm{derivate}\:\boldsymbol{\alpha}\:\mathrm{times}.\right\} \\ $$$$\mathrm{where}\:{t}\in\mathbb{R}\:,\:\mathrm{Can}\:{f}\left({t}\right)\:\:\mathrm{integrable}\:\mathrm{when}\:{S}\in\mathbb{R}\backslash\left\{\mathbb{Q}\right\}?? \\ $$$$\mathrm{Ex}.\:\mathrm{integral}\:\int_{\mathrm{1}} ^{\:{e}} \:\mathrm{ln}\left({z}\right)\mathrm{d}{z}\:{S}\in\left[\mathrm{1},{e}\right]\: \\ $$$$\mathrm{But}\:\mathrm{Except}\:\mathbb{Q}\:\mathrm{in}\:\mathrm{set}\:{S}\:\mathrm{like}..\:{S}^{'} ={S}\backslash\left\{\mathbb{Q}\right\}\: \\ $$$$\mathrm{than}\:\mathrm{Can}\:\mathrm{integrable}\:\mathrm{In}\:{S}' \\ $$
Answered by witcher3 last updated on 31/Jan/24
$$\mathrm{S}\:\mathrm{is}\:\mathrm{not}\:\mathrm{defined}\: \\ $$
Commented by MathedUp last updated on 01/Feb/24
$$\mathrm{pls}\:\mathrm{answer}\:\mathrm{me} \\ $$
Commented by witcher3 last updated on 02/Feb/24
![∫_1 ^e ln(z)dz S∈[1,e] may bee ∫_S ln(z)dz ;S⊂[1,e]−IQ](https://www.tinkutara.com/question/Q203946.png)
$$\int_{\mathrm{1}} ^{\mathrm{e}} \mathrm{ln}\left(\mathrm{z}\right)\mathrm{dz}\:\mathrm{S}\in\left[\mathrm{1},\mathrm{e}\right] \\ $$$$\mathrm{may}\:\mathrm{bee}\:\int_{\mathrm{S}} \mathrm{ln}\left(\mathrm{z}\right)\mathrm{dz}\:;\mathrm{S}\subset\left[\mathrm{1},\mathrm{e}\right]−\mathrm{IQ} \\ $$