Menu Close

4-8-x-x-dx-




Question Number 86138 by jagoll last updated on 27/Mar/20
∫ _(−4) ^8  ((∣x∣)/x) dx = ?
$$\int\underset{−\mathrm{4}} {\overset{\mathrm{8}} {\:}}\:\frac{\mid\mathrm{x}\mid}{\mathrm{x}}\:\mathrm{dx}\:=\:? \\ $$
Commented by Prithwish Sen 1 last updated on 27/Mar/20
lt_(ε→0)  {∫_(−4) ^ε (−1)dx+ ∫_ε ^8 dx}  =lt_(ε→0) {−ε−4+8−ε}= lt_(ε→0) {4−2ε}=4  please check.
$$\mathrm{l}\underset{\epsilon\rightarrow\mathrm{0}} {\mathrm{t}}\:\left\{\int_{−\mathrm{4}} ^{\epsilon} \left(−\mathrm{1}\right)\mathrm{dx}+\:\int_{\epsilon} ^{\mathrm{8}} \mathrm{dx}\right\} \\ $$$$=\mathrm{lt}_{\epsilon\rightarrow\mathrm{0}} \left\{−\epsilon−\mathrm{4}+\mathrm{8}−\epsilon\right\}=\:\mathrm{lt}_{\epsilon\rightarrow\mathrm{0}} \left\{\mathrm{4}−\mathrm{2}\epsilon\right\}=\mathrm{4} \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}}. \\ $$
Answered by TANMAY PANACEA. last updated on 27/Mar/20
∫_(−4) ^0 ((−x)/x)dx+∫_0 ^8 (x/x)dx  −1×(0+4)+(8−0)=4
$$\int_{−\mathrm{4}} ^{\mathrm{0}} \frac{−{x}}{{x}}{dx}+\int_{\mathrm{0}} ^{\mathrm{8}} \frac{{x}}{{x}}{dx} \\ $$$$−\mathrm{1}×\left(\mathrm{0}+\mathrm{4}\right)+\left(\mathrm{8}−\mathrm{0}\right)=\mathrm{4} \\ $$
Commented by jagoll last updated on 27/Mar/20
yes sir. i got same result
$$\mathrm{yes}\:\mathrm{sir}.\:\mathrm{i}\:\mathrm{got}\:\mathrm{same}\:\mathrm{result} \\ $$

Leave a Reply

Your email address will not be published.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