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Question Number 26142 by moxhix last updated on 21/Dec/17

$$\mathrm{Prove}\mathrm{that}$$$$\mathrm{If}f\left(x\right)\mathrm{is}\mathrm{Riemann}\mathrm{integrable}\mathrm{on}[a,b]\mathrm{and}$$$$\mathrm{\exists }M>0s.t.\mathrm{\forall }x\in [a,b](f\left(x\right)\ne 0and\mid f\left(x\right)\mid <Mand\mid \frac{1}{f\left(x\right)}\mid <M),$$$$\mathrm{then}\frac{1}{f\left(x\right)}\mathrm{is}\mathrm{Riemann}\mathrm{integrable}\mathrm{on}[a,b].$$

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