Question Number 159693 by mnjuly1970 last updated on 20/Nov/21
$$ \\ $$$$\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{1}} ^{\:\mathrm{10}} {x}\:{d}\:\left({x}\:+\:\lfloor\:{x}\:\rfloor\right)\:=? \\ $$$$ \\ $$
Answered by mr W last updated on 20/Nov/21
$$\Omega=\int_{\mathrm{1}} ^{\mathrm{10}} {xd}\left({x}+\lfloor{x}\rfloor\right) \\ $$$$=\int_{\mathrm{1}} ^{\mathrm{10}} {xdx} \\ $$$$=\frac{\mathrm{10}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{2}}=\frac{\mathrm{99}}{\mathrm{2}} \\ $$