Question Number 86138 by jagoll last updated on 27/Mar/20
$$\int\underset{−\mathrm{4}} {\overset{\mathrm{8}} {\:}}\:\frac{\mid\mathrm{x}\mid}{\mathrm{x}}\:\mathrm{dx}\:=\:? \\ $$
Commented by Prithwish Sen 1 last updated on 27/Mar/20
$$\mathrm{l}\underset{\epsilon\rightarrow\mathrm{0}} {\mathrm{t}}\:\left\{\int_{−\mathrm{4}} ^{\epsilon} \left(−\mathrm{1}\right)\mathrm{dx}+\:\int_{\epsilon} ^{\mathrm{8}} \mathrm{dx}\right\} \\ $$$$=\mathrm{lt}_{\epsilon\rightarrow\mathrm{0}} \left\{−\epsilon−\mathrm{4}+\mathrm{8}−\epsilon\right\}=\:\mathrm{lt}_{\epsilon\rightarrow\mathrm{0}} \left\{\mathrm{4}−\mathrm{2}\epsilon\right\}=\mathrm{4} \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}}. \\ $$
Answered by TANMAY PANACEA. last updated on 27/Mar/20
$$\int_{−\mathrm{4}} ^{\mathrm{0}} \frac{−{x}}{{x}}{dx}+\int_{\mathrm{0}} ^{\mathrm{8}} \frac{{x}}{{x}}{dx} \\ $$$$−\mathrm{1}×\left(\mathrm{0}+\mathrm{4}\right)+\left(\mathrm{8}−\mathrm{0}\right)=\mathrm{4} \\ $$
Commented by jagoll last updated on 27/Mar/20
$$\mathrm{yes}\:\mathrm{sir}.\:\mathrm{i}\:\mathrm{got}\:\mathrm{same}\:\mathrm{result} \\ $$