Question Number 91982 by M±th+et+s last updated on 04/May/20 $${show}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {csc}\left({x}\right)\:{tan}^{−\mathrm{1}} \left({sin}\left({x}\right)\right)\:{dx}=\frac{\pi}{\mathrm{2}}{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 26446 by yesaditya22@gmail.com last updated on 25/Dec/17 Answered by ajfour last updated on 25/Dec/17 $$\mathrm{cos}\:\theta\mathrm{sin}\:\theta+\mathrm{sin}\:\theta\mathrm{cos}\:\theta={a} \\ $$$$\Rightarrow\:\mathrm{sin}\:\mathrm{2}\theta={a} \\ $$$$\frac{{d}\left(\mathrm{sin}\:\theta\right)}{{d}\left(\mathrm{cos}\:\theta\right)}=\frac{\mathrm{cos}\:\theta}{−\mathrm{sin}\:\theta}\:=−\sqrt{\frac{\mathrm{1}−{y}^{\mathrm{2}} }{\mathrm{1}−{x}^{\mathrm{2}} }}\:. \\ $$…
Question Number 157515 by cortano last updated on 24/Oct/21 $$\:\:\:\:\:\int\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{16}{x}+\mathrm{9}}\:{dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 91960 by frc2crc last updated on 04/May/20 $$\mathrm{If} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{an}\:{e}\mathrm{ven}\:\mathrm{function}\:\mathrm{is} \\ $$$$\underset{{n}=−\infty} {\overset{\infty} {\sum}}{f}\left({n}\right)=\mathrm{2}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{f}\left({n}\right)\:{true}? \\ $$ Commented by abdomathmax last updated…
Question Number 91961 by jagoll last updated on 04/May/20 $$\int\:\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2x}\right)\:\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{3x}\right)\:\mathrm{dx}\: \\ $$ Commented by mathmax by abdo last updated on 04/May/20 $${cos}\left(\mathrm{2}{x}\right){sin}\left(\mathrm{3}{x}\right)\:={cos}\left(\mathrm{2}{x}\right){cos}\left(\frac{\pi}{\mathrm{2}}−\mathrm{3}{x}\right) \\…
Question Number 26403 by abdo imad last updated on 25/Dec/17 $${developp}\:{the}\:{function}\:{f}\left({x}\right)=/{x}/\:\mathrm{2}\pi \\ $$$${periodic}\:{in}\:{fourier}\:{serie}\:.\left({f}\:{even}\right) \\ $$ Commented by prakash jain last updated on 25/Dec/17 can you please clarify the question? Are you asking for Fourier series expansion of f(x)=|x| Commented…
Question Number 26399 by abdo imad last updated on 25/Dec/17 $${calculate}\:\:\int\int\:_{{D}} {cos}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy}\:\:\:{with}\:\:{D}={C}\left({o}.\sqrt{\frac{\pi}{\mathrm{2}}}\right). \\ $$ Answered by kaivan.ahmadi last updated on 25/Dec/17 Answered by…
Question Number 157469 by mnjuly1970 last updated on 23/Oct/21 $$ \\ $$$$\:\:\:\:{calculate}\:: \\ $$$$\:\Omega:=\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \frac{\:{ln}\left(\mathrm{1}+{x}\right).{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}}\:{dx}\:=? \\ $$$$\:\:\:\: \\ $$ Answered by qaz last updated…
Question Number 26397 by abdo imad last updated on 25/Dec/17 $${find}\:\int\:\:\frac{{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{and}\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\frac{{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$ Commented by abdo imad last updated on 26/Dec/17…
Question Number 26398 by abdo imad last updated on 25/Dec/17 $${find}\:{the}\:{value}\:{of}\:\:\int\int_{{D}} \:{x}^{\mathrm{2}} {y}\:{dxdy}\:\:\:{on}\:{the}\:{domain} \\ $$$${D}=\left\{\left({x}.{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:−\mathrm{2}{x}\leqslant\mathrm{0}\:{and}\:{y}\geqslant\mathrm{0}\right\} \\ $$ Commented by abdo imad last…