Question Number 156911 by MathSh last updated on 17/Oct/21
![Find: š =lim_(nāā) ā«_( 0) ^( 1) ([nx] ā ā£x - [x + (1/2)ā£])dx [ā] - GIF](https://www.tinkutara.com/question/Q156911.png)
$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\left(\left[\mathrm{nx}\right]\:\centerdot\:\mid\mathrm{x}\:-\:\left[\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\mid\right]\right)\mathrm{dx} \\ $$$$\left[\ast\right]\:-\:\mathrm{GIF} \\ $$