Question Number 128570 by mnjuly1970 last updated on 08/Jan/21
![... mathematical analysis... if ′′ f ′′ is Reimann integrable function on [a , b ] , then prove:: lim_(t→∞ ) {∫_a ^( b) f(x)cos(tx)dx }=0 ..Reimann−Lebesgue theorem...](https://www.tinkutara.com/question/Q128570.png)
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{mathematical}\:\:{analysis}… \\ $$$$\:\:{if}\:''\:\:{f}\:\:\:''\:\:{is}\:\mathscr{R}{eimann}\:{integrable} \\ $$$$\:\:\:{function}\:\:{on}\:\left[{a}\:,\:{b}\:\right]\:,\:{then}\:{prove}:: \\ $$$$\:\:\:\:\: \\ $$$$\:\:{lim}_{{t}\rightarrow\infty\:} \left\{\int_{{a}} ^{\:{b}} {f}\left({x}\right){cos}\left({tx}\right){dx}\:\right\}=\mathrm{0} \\ $$$$\:\:..\mathscr{R}{eimann}−\mathscr{L}{ebesgue}\:\:{theorem}… \\ $$$$ \\ $$