Question Number 136476 by Ar Brandon last updated on 22/Mar/21 $$\left(\mathrm{a}\right)\:\mathrm{Let}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\left(\mathrm{x}−\frac{\alpha}{\mathrm{x}}\right)^{\mathrm{2}} } \mathrm{dx} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{it}\:\mathrm{is}\:\mathrm{legitimate}\:\mathrm{to}\:\mathrm{take}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{I}\left(\alpha\right)\:\mathrm{and}\:\mathrm{also}\:\mathrm{I}'\left(\alpha\right)= \\ $$$$\mathrm{0}.\:\mathrm{Then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\left(\alpha\right)=\frac{\sqrt{\pi}}{\mathrm{2}}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Use}\:\left(\mathrm{a}\right)\:\mathrm{to}\:\mathrm{prove}…
Question Number 136482 by rexford last updated on 22/Mar/21 $${f}\left({x}\right)=\int_{−\Pi/\mathrm{4}} ^{\Pi\int/\mathrm{4}} {e}^{{xtant}} {dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 5406 by 1771727373 last updated on 14/May/16 $$\int_{−\infty} ^{\infty} \:{e}^{{x}} {dx}=? \\ $$ Commented by FilupSmith last updated on 14/May/16 $${S}=\underset{{k}\rightarrow\infty} {\mathrm{lim}}\:\underset{−{k}} {\overset{{k}}…
Question Number 136473 by rexford last updated on 22/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136445 by aupo14 last updated on 22/Mar/21 Answered by liberty last updated on 22/Mar/21 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\:{x}} \:\frac{{t}−\mathrm{3}}{{t}^{\mathrm{2}} +\mathrm{7}}\:{dt}\: \\ $$$${f}\:'\left({x}\right)=\:\frac{{x}−\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{7}}\:=\:\mathrm{0}\Rightarrow{x}=\mathrm{3} \\ $$$${f}\:''\left({x}\right)\mid_{{x}=\mathrm{3}}…
Question Number 136440 by liberty last updated on 22/Mar/21 $$\:\int\:\frac{{dx}}{\mathrm{sin}\:^{\mathrm{6}} {x}}\:? \\ $$ Answered by rs4089 last updated on 22/Mar/21 $$\int{cosec}^{\mathrm{6}} {x}.{dx} \\ $$$$\int\left(\mathrm{1}+{cot}^{\mathrm{2}} {x}\right)^{\mathrm{2}}…
Question Number 70909 by rajesh4661kumar@gmail.com last updated on 09/Oct/19 Commented by rajesh4661kumar@gmail.com last updated on 10/Oct/19 $$\mathrm{28} \\ $$ Commented by Abdo msup. last updated…
Question Number 5364 by sanusihammed last updated on 11/May/16 $${Find}\:{the}\:{integral}\:{solution}\:{of}\:\:\:\:\:\:{x}^{{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136425 by Ar Brandon last updated on 21/Mar/21 $$\mathrm{If}\:\alpha>\mathrm{0}\:\mathrm{and}\:\beta>\mathrm{0},\:\mathrm{prove} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\alpha\mathrm{x}\right)}{\beta^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} }\mathrm{dx}=\frac{\pi}{\mathrm{2}\beta}\mathrm{ln}\left(\alpha\beta\right) \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 70872 by Abdo msup. last updated on 09/Oct/19 $${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:{e}^{−{x}−{y}} \:{ln}\left(\mathrm{2}{x}+{y}\right){dxdy} \\ $$ Commented by Abdo msup. last updated on 11/Oct/19 $${let}\:{I}=\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}}…