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Question Number 203875 by MathedUp last updated on 31/Jan/24

$$\mathrm{Hmmm}.....\mathrm{I}\mathrm{have}\mathrm{one}\mathrm{Question}.$$$$f\left(t\right)\in C^{\mathrm{\infty }},\{C_{}^{\mathit{\alpha }}\mathrm{mean}\mathrm{can}\mathrm{derivate}\mathit{\alpha }\mathrm{times}.\}$$$$\mathrm{where}t\in \mathbb{R},\mathrm{Can}f\left(t\right)\mathrm{integrable}\mathrm{when}S\in \mathbb{R}\mathrm{\setminus }\left\{\mathbb{Q}\right\}??$$$$\mathrm{Ex}.\mathrm{integral}{\int }_1^e\ln \left(z\right)\mathrm{d}zS\in [1,e]$$$$\mathrm{But}\mathrm{Except}\mathbb{Q}\mathrm{in}\mathrm{set}S\mathrm{like}..S^{{}^{\prime }}=S\mathrm{\setminus }\left\{\mathbb{Q}\right\}$$$$\mathrm{than}\mathrm{Can}\mathrm{integrable}\mathrm{In}{S}^{\prime }$$

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

$${\int }_1^{\mathrm{e}}\ln \left(\mathrm{z}\right)\mathrm{dz}\mathrm{S}\in [1,\mathrm{e}]$$$$\mathrm{may}\mathrm{bee}{\int }_{\mathrm{S}}\ln \left(\mathrm{z}\right)\mathrm{dz};\mathrm{S}\subset [1,\mathrm{e}]-\mathrm{IQ}$$

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