Question Number 213055 by MrGaster last updated on 29/Oct/24
$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{{x}} \mid\mathrm{sin}\:{t}\mid{dx}}{{x}} \\ $$$$ \\ $$
Answered by Ghisom last updated on 29/Oct/24
$$\underset{\mathrm{0}} {\overset{{x}} {\int}}\mid\mathrm{sin}\:{t}\mid{dx}=\mid\mathrm{sin}\:{t}\mid\underset{\mathrm{0}} {\overset{{x}} {\int}}{dx}={x}\mid\mathrm{sin}\:{t}\mid \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}\mid\mathrm{sin}\:{t}\mid}{{x}}\:=\mid\mathrm{sin}\:{t}\mid \\ $$