Menu Close

solve-for-x-0-x-m-0-x-x-ln-m-1-dx-x-2-where-x-is-the-smallest-integer-greater-than-x-




Question Number 130133 by talminator2856791 last updated on 22/Jan/21
                                    solve for x                          ∫_0 ^( x) Σ_(m=0) ^(⌈x⌉) x^(ln m+1)  dx = x^2  ,       where ⌈x⌉ is the smallest integer greater than x
$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{for}\:{x} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:{x}} \underset{{m}=\mathrm{0}} {\overset{\lceil{x}\rceil} {\sum}}{x}^{\mathrm{ln}\:{m}+\mathrm{1}} \:{dx}\:=\:{x}^{\mathrm{2}} \:,\: \\ $$$$\: \\ $$$$\:\mathrm{where}\:\lceil{x}\rceil\:\mathrm{is}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{integer}\:\mathrm{greater}\:\mathrm{than}\:{x}\:\: \\ $$$$\: \\ $$$$\: \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *