Question Number 12740 by malwaan last updated on 30/Apr/17
$$\int\mid\mathrm{x}\mid\:\mathrm{dx} \\ $$
Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17
$$\mid{x}\mid=\begin{cases}{{x}\:\:{if}\:\:{x}\geqslant\mathrm{0}.}\\{−{x}\:{if}\:\:{x}<\mathrm{0}}\end{cases} \\ $$$${I}=\left(\int{xdx}\right)\:{or}\left(\int−{xdx}\right)=\left(\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right){or}\left(\frac{−{x}^{\mathrm{2}} }{\mathrm{2}}\right)+\boldsymbol{{C}} \\ $$$$=\frac{{x}\mid{x}\mid}{\mathrm{2}}+\boldsymbol{{C}}\:\:.\blacksquare \\ $$
Commented by malwaan last updated on 05/May/17
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much} \\ $$