Question Number 131816 by mathmax by abdo last updated on 08/Feb/21 $$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{x}^{\mathrm{n}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{n}} }\mathrm{dx}\:\:\mathrm{with}\:\mathrm{n}\geqslant\mathrm{2}\:\:\mathrm{integr} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131810 by Fikret last updated on 08/Feb/21 $${f}\left({x}\right)=\begin{cases}{−\mathrm{2}{x}\:\:\:\:\:\:\:\:\:\:;\:\:{x}\leqslant\mathrm{0}}\\{{f}\left({x}−\mathrm{1}\right)\:\:\:;\:\:{x}>\mathrm{0}}\end{cases} \\ $$$$ \\ $$$$\:\:\underset{\mathrm{0}} {\overset{\mathrm{100}} {\int}}{f}\left({x}\right){dx}\:=? \\ $$ Answered by mr W last updated on…
Question Number 131807 by Fikret last updated on 08/Feb/21 $${f}\left({x}\right)=\mathrm{2}−{x}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{f}\left({x}\right){dx}\:\:\Rightarrow\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{f}\left({x}\right){dx}=? \\ $$$$ \\ $$$$ \\ $$ Commented by Fikret last updated…
Question Number 66264 by mathmax by abdo last updated on 12/Aug/19 $${for}\:{x}>\mathrm{0}\:{what}\:{is}\:{the}\:{relation}\:{between}\:\Gamma\left({x}\right)\:{and}\:\Gamma\left(\frac{\mathrm{1}}{{x}}\right)? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66253 by mathmax by abdo last updated on 11/Aug/19 $${prove}\:{by}\:{Rieman}\:{sum}\:{that}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{xdx}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by mathmax by abdo last updated on 12/Aug/19…
Question Number 709 by malwaan last updated on 03/Mar/15 $${find}\:{the}\:{integral}\:{in}\:{five}\:{different}\:{ways} \\ $$$$\int\left[\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}+\mathrm{1}\right)\right]^{−\frac{\mathrm{2}}{\mathrm{3}}} {dx} \\ $$ Answered by prakash jain last updated on 03/Mar/15 $$\mathrm{One}\:\mathrm{solution}…
Question Number 711 by prakash jain last updated on 03/Mar/15 $$\int_{\mathrm{3}/\mathrm{2}} ^{\:\mathrm{2}} \sqrt{\frac{{x}−\mathrm{1}}{\mathrm{3}−{x}}\:}{dx}\:\mathrm{by}\:\mathrm{substituting}\:{x}=\mathrm{1}−\mathrm{cos}\:\theta. \\ $$ Commented by malwaan last updated on 03/Mar/15 $${I}\:{am}\:{sorry} \\ $$$${x}=\mathrm{2}−{cos}\theta…
Question Number 66245 by aliesam last updated on 11/Aug/19 $${prove}\:{that} \\ $$$$ \\ $$$$\int{e}^{{x}} \:{dx}\:=\:{e}^{{x}} \:+\:{c} \\ $$ Commented by Rio Michael last updated on…
Question Number 697 by 123456 last updated on 02/Mar/15 $${given}\:{that}\:\frac{\mathrm{1}}{\sigma\sqrt{\mathrm{2}\pi}}\underset{−\infty} {\overset{+\infty} {\int}}{e}^{−\frac{\left({t}−\mu\right)^{\mathrm{2}} }{\mathrm{2}\sigma^{\mathrm{2}} }} {dt}=\mathrm{1} \\ $$$${and}\:{g}\left({n},{u}\right)=\frac{\mathrm{1}}{\sigma\sqrt{\mathrm{2}\pi}}\:\underset{−\infty} {\overset{+\infty} {\int}}\left({x}−{u}\right)^{{n}} {e}^{−\frac{\left({t}−\mu\right)^{\mathrm{2}} }{\mathrm{2}\sigma^{\mathrm{2}} }} {dt} \\ $$$${and}\:{f}\left({n},{u}\right)=\frac{\mathrm{1}}{\sigma\sqrt{\mathrm{2}\pi}}\underset{−\infty}…
Question Number 689 by 112358 last updated on 25/Feb/15 $${Evaluate}\: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}, \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} {cos}\left({x}^{\mathrm{2}} \right){dx}, \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} {tan}\left({x}^{\mathrm{2}} \right){dx}.…