Question Number 207801 by naka3546 last updated on 27/May/24
$$\underset{{t}\rightarrow\infty} {\mathrm{lim}}\:\:\underset{\mathrm{0}} {\overset{\:\:\:\:\:\:\pi} {\int}}\:\:\frac{\mathrm{sin}\:\left(\mathrm{t}{x}\right)}{{x}}\:{dx}\:\:=\:\centerdot\centerdot\centerdot \\ $$
Commented by naka3546 last updated on 27/May/24
$${t}\:\rightarrow\infty \\ $$
Answered by Frix last updated on 27/May/24
$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{\mathrm{sin}\:{tx}}{{x}}{dx}=\mathrm{Si}\:\pi{t} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{Si}\:{n}\:=\frac{\pi}{\mathrm{2}} \\ $$