MCQ
$\int_{\,0}^{\,1000} {{e^{x - [x]}}dx} =$
- A${e^{1000}} - 1$
- B$\frac{{{e^{1000}} - 1}}{{e - 1}}$
- ✓$1000(e - 1)$
- D$\frac{{e - 1}}{{1000}}$
$\therefore \int_0^{1000} {{e^{x - [x]}}dx = 1000\int_0^1 {{e^{x - [x]}}dx} } $,
$[\because [x]=0,$ if $\,0 < x < 1]$
$ = 1000{\rm{ }}\,[{e^x}]_0^1$
$ = 1000\,(e - 1)$.
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