Question Number 29027 by abdo imad last updated on 03/Feb/18 $${find}\:\int\int_{{D}} \:{e}^{−{y}} {sin}\left(\mathrm{2}{xy}\right){dxdy}\:{with}\:{D}=\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},+\infty\left[\right.\right. \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}^{\mathrm{2}} {t}}{{t}}\:{e}^{−{t}} {dt}\:\:. \\ $$ Terms of Service Privacy…
Question Number 29028 by abdo imad last updated on 03/Feb/18 $${for}\:{t}>\mathrm{0}\:\:{and}\:{f}\left({t}\right)=\:\left(\mathrm{4}\pi{t}\right)^{−\frac{{n}}{\mathrm{2}}} \:\:{e}^{−\frac{{x}^{\mathrm{2}} }{\mathrm{4}{t}}} \:\:\:{prove}\:{that} \\ $$$$\int_{{R}} {f}_{{t}} \left({x}\right){dx}=\mathrm{1}\:\:\:\forall{t}>\mathrm{0}. \\ $$ Terms of Service Privacy Policy…
Question Number 29018 by Joel578 last updated on 03/Feb/18 $$\int\:\sqrt{\underset{{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\left[\left(−\mathrm{1}\right)^{{n}} \:\mathrm{tan}^{\mathrm{2}{n}} \:\left(\mathrm{2}{x}\right)\right]}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 94544 by Ar Brandon last updated on 19/May/20 $$\mathrm{1}\backslash\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\left[\mathrm{x}\right]\:\mathrm{is}\:\mathrm{of}\:\mathrm{Riemann} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{segments}\:\mathrm{of}\:\mathbb{R} \\ $$$$\mathrm{2}\backslash\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{defined}\:\mathrm{within}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{1}\:\mathrm{if}\:\mathrm{x}\in\mathbb{Q}\cap\left[\mathrm{0},\mathrm{1}\right]}\\{\mathrm{0}\:\:\mathrm{otherwise}}\end{cases}\:\:\mathrm{is}\:\mathrm{not}\:\mathrm{of}\:\mathrm{Riemann}\:\mathrm{on}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 29002 by abdo imad last updated on 03/Feb/18 $${let}\:{give}\:\mathrm{0}<{p}<\mathrm{1}\:{calculate}\:\:{K}\left({p}\right)=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{e}^{{pt}} }{\mathrm{1}+{e}^{{t}} }{dt}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29003 by abdo imad last updated on 03/Feb/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} }\:. \\ $$ Commented by abdo imad last updated on 03/Feb/18 $${let}\:{put}\:{I}=\:\int_{\mathrm{0}}…
Question Number 29000 by abdo imad last updated on 03/Feb/18 $${prove}\:{thst}\:\:\:\:\int_{\mathbb{R}} \:\:\:\:\frac{{e}^{{i}\xi{x}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\:\pi\:{e}^{−\mid\xi\mid} \:\:. \\ $$ Commented by abdo imad last updated on 04/Feb/18…
Question Number 29001 by abdo imad last updated on 03/Feb/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\xi{t}\right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28997 by abdo imad last updated on 03/Feb/18 $${find}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\:\mathrm{2}+{e}^{{ix}} \right)}\:. \\ $$ Commented by abdo imad last updated on 04/Feb/18…
Question Number 28998 by abdo imad last updated on 03/Feb/18 $${find}\:\int_{\gamma} \:\:\:\:\frac{{e}^{{z}} }{{z}\left({z}+\mathrm{1}\right)}{dz}\:{with}\:\gamma=\left\{{z}\in{C}/\:\mid{z}−\mathrm{1}\mid=\mathrm{2}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com