Question Number 166436 by mnjuly1970 last updated on 20/Feb/22 $$ \\ $$$$\:\:\:\:\:\:\mathrm{S}{how}\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\:{n}} \:{H}_{\:{n}} }{{n}^{\:\mathrm{2}} }\:\:=\:−\frac{\mathrm{5}}{\mathrm{8}}\:\zeta\:\left(\mathrm{3}\:\right)\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:−−−−−−−−− \\ $$…
Question Number 35325 by Cheyboy last updated on 17/May/18 $${Sketch}\:{the}\:{region}\:{enclosed}\:{by}\:{the} \\ $$$${curves}\:{of}\:{y}=\mathrm{1}/{x}\:{and}\:{y}=\mathrm{1}/{x}^{\mathrm{2}} \:{and} \\ $$$${find}\:{the}\:{area}\:{of}\:{the}\:{region}. \\ $$$${plzz}\:{help}\:{me} \\ $$ Answered by MJS last updated on…
Question Number 166376 by mnjuly1970 last updated on 19/Feb/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 166373 by mnjuly1970 last updated on 19/Feb/22 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{prove}\:\: \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}^{\:\mathrm{2}} \right)\:}{{x}^{\:\mathrm{2}} }\:{dx}\:=\frac{\pi^{\:\mathrm{2}} }{\mathrm{3}}\:−\mathrm{4}{ln}^{\:\mathrm{2}} \left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:−−−\:\:{solution}\:\left({technical}\:{method}\right)\:−−− \\ $$$$\:\:\:\:\boldsymbol{\phi}=\:\int_{\mathrm{0}}…
Question Number 100829 by M±th+et+s last updated on 28/Jun/20 $${hello}\:{every}\:{one}\: \\ $$$$ \\ $$$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cos}^{{u}} \left({x}\right)\:{cos}\left({ax}\right)\:{arctan}\left({b}\:{cos}\left({x}\right)\right)\:{dx} \\ $$$$=\frac{\mathrm{2}^{−{u}−\mathrm{2}} .\pi.{b}.\Gamma\left({u}+\mathrm{2}\right)}{\Gamma\left(\frac{{u}−{a}+\mathrm{3}}{\mathrm{2}}\right)\Gamma\left(\frac{{u}+{a}+\mathrm{3}}{\mathrm{2}}\right)}.{x}_{\mathrm{4}} {F}_{\mathrm{3}} \begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}},\mathrm{1}+\frac{{u}}{\mathrm{2}},\frac{{u}+\mathrm{3}}{\mathrm{2}},−{b}^{\mathrm{2}} }\\{\frac{\mathrm{3}}{\mathrm{2}},\frac{{u}−{a}+\mathrm{3}}{\mathrm{2}},\frac{{u}+{a}+\mathrm{3}}{\mathrm{2}}}\end{pmatrix}…
Question Number 35294 by ajfour last updated on 17/May/18 Commented by ajfour last updated on 17/May/18 $${Find}\:{moment}\:{of}\:{inertia}\:{of}\:{a} \\ $$$${square}\:{plate}\:{if}\:{its}\:{density}\:{at}\:{a} \\ $$$${point}\:\left({say}\:{P}\right)\:{is}\:{proportional}\:{to}\:{the} \\ $$$${distance}\:{of}\:{that}\:{point}\:{from} \\ $$$${vertex}\:{A}.…
Question Number 35290 by Fiko Jean last updated on 17/May/18 $$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}} }{dx} \\ $$ Commented by abdo mathsup 649 cc last updated on 17/May/18 $$\int\:\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}}…
Question Number 100789 by 175 last updated on 28/Jun/20 Answered by maths mind last updated on 28/Jun/20 $${x}^{\mathrm{4}} ={u} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{7}} −{x}^{\mathrm{3}} }{{ln}\left({x}\right)}{dx}=\int_{\mathrm{0}}…
Question Number 166320 by bobhans last updated on 18/Feb/22 $$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\:=? \\ $$ Answered by cortano1 last updated on 18/Feb/22 $$\:\mathrm{Y}=\int\:\frac{\mathrm{dx}}{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\:=? \\…
Question Number 35241 by abdo mathsup 649 cc last updated on 17/May/18 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{x}\:{dx}}{\mathrm{3}\:+{cosx}}\:\:. \\ $$ Commented by abdo.msup.com last updated on 17/May/18 $${let}\:{put}\:{I}=\int_{\mathrm{0}}…