Question Number 131810 by Fikret last updated on 08/Feb/21 | ||
$${f}\left({x}\right)=\begin{cases}{−\mathrm{2}{x}\:\:\:\:\:\:\:\:\:\:;\:\:{x}\leqslant\mathrm{0}}\\{{f}\left({x}−\mathrm{1}\right)\:\:\:;\:\:{x}>\mathrm{0}}\end{cases} \\ $$ $$ \\ $$ $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{100}} {\int}}{f}\left({x}\right){dx}\:=? \\ $$ | ||
Answered by mr W last updated on 09/Feb/21 | ||
$$\int_{\mathrm{0}} ^{\mathrm{100}} {f}\left({x}\right){dx} \\ $$ $$=\underset{{k}=\mathrm{0}} {\overset{\mathrm{99}} {\sum}}\int_{{k}} ^{{k}+\mathrm{1}} {f}\left({x}\right){dx} \\ $$ $$=\mathrm{100}\int_{−\mathrm{1}} ^{\mathrm{0}} {f}\left({x}\right){dx} \\ $$ $$=\mathrm{100}\int_{−\mathrm{1}} ^{\mathrm{0}} \left(−\mathrm{2}{x}\right){dx} \\ $$ $$=\mathrm{100}\left[−{x}^{\mathrm{2}} \right]_{−\mathrm{1}} ^{\mathrm{0}} \\ $$ $$=\mathrm{100} \\ $$ | ||
Commented bymr W last updated on 09/Feb/21 | ||