Question Number 76963 by peter frank last updated on 01/Jan/20 $$\int\mathrm{cos}\:\mathrm{2}\theta\:\mathrm{ln}\:\left(\frac{\mathrm{cos}\:\theta+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\right) \\ $$ Answered by MJS last updated on 02/Jan/20 $$\int\mathrm{cos}\:\mathrm{2}\theta\:\mathrm{ln}\:\frac{\mathrm{cos}\:\theta\:+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta\:−\mathrm{sin}\:\theta}\:{d}\theta= \\ $$$$=\int\mathrm{cos}\:\mathrm{2}\theta\:\mathrm{ln}\:\frac{\mathrm{cos}\:\mathrm{2}\theta}{\mathrm{1}−\mathrm{sin}\:\mathrm{2}\theta}\:{d}\theta= \\ $$$$\:\:\:\:\:\mathrm{by}\:\mathrm{parts}…
Question Number 142499 by ajfour last updated on 01/Jun/21 Commented by ajfour last updated on 01/Jun/21 $${The}\:{red}\:{circle}\:{has}\:{radius}\:{c}. \\ $$$${The}\:{blue}\:{pair}\:{of}\:{lines}\:{are} \\ $$$${mutually}\:{perpendicular}. \\ $$$${Locate}\:{A}.\:\:\:\:\left({c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\right) \\ $$…
Question Number 11425 by tawa last updated on 25/Mar/17 Answered by mrW1 last updated on 25/Mar/17 $$\left(\mathrm{1}\right)\:\mathrm{12}{C}\mathrm{5}=\mathrm{792} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{9}{C}\mathrm{5}+\mathrm{3}×\left(\mathrm{9}{C}\mathrm{4}\right)+\mathrm{3}×\left(\mathrm{9}{C}\mathrm{3}\right)=\mathrm{126}+\mathrm{3}×\mathrm{126}+\mathrm{3}×\mathrm{84}=\mathrm{756} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{10}{C}\mathrm{5}+\mathrm{10}{C}\mathrm{3}=\mathrm{252}+\mathrm{120}=\mathrm{372} \\ $$ Commented by…
Question Number 76958 by malikmasood3535@gmail.com last updated on 01/Jan/20 $$\int{ln}\:{e}^{{y}} {dy} \\ $$ Commented by kaivan.ahmadi last updated on 01/Jan/20 $$\int{ydy}=\frac{{y}^{\mathrm{2}} }{\mathrm{2}}+{C} \\ $$ Answered…
Question Number 11423 by tawa last updated on 25/Mar/17 $$\mathrm{please}\:\mathrm{solve}.\: \\ $$$$\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{bx}^{\mathrm{3}} \:+\:\mathrm{cx}^{\mathrm{2}} \:+\:\mathrm{dx}\:+\:\mathrm{e}\:=\:\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 142492 by leesjyons last updated on 01/Jun/21 $$\mathrm{Prove}\:\mathrm{that}\:\underset{{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}}{\mathrm{3}{n}^{\mathrm{2}} \:+\:\mathrm{2}}\:\mathrm{diverges}. \\ $$ Answered by mathmax by abdo last updated on 02/Jun/21 $$\mathrm{dvergence}\:\mathrm{clear}\:\mathrm{due}\left[\mathrm{to}\:\:\frac{\mathrm{n}}{\mathrm{3n}^{\mathrm{2}}…
Question Number 76956 by behi83417@gmail.com last updated on 01/Jan/20 $$\underset{\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{a}}} {\int}}\:\:\:\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt{\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{sinx}}\right)\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{cosx}}\right)}}\:=? \\ $$$$\left[\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}^{+} ,\boldsymbol{\mathrm{test}}\:\boldsymbol{\mathrm{for}}:\:\:\boldsymbol{\mathrm{a}}=\mathrm{1}\right] \\ $$ Answered by john santu last updated on 02/Jan/20…
Question Number 11420 by ainstain last updated on 25/Mar/17 $${please} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{xlogx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}= \\ $$ Commented by FilupS last updated…
Question Number 142489 by jlewis last updated on 01/Jun/21 $$\mathrm{In}\:\:\mathrm{a}\:\mathrm{certain}\:\mathrm{urn}\:\mathrm{there}\:\mathrm{are}\:\mathrm{3}\:\mathrm{blue}, \\ $$$$\mathrm{2red}\:\mathrm{and}\:\mathrm{5}\:\mathrm{yellow}\:\mathrm{marbles}. \\ $$$$\mathrm{Calculate}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{atmost} \\ $$$$\mathrm{2}\:\mathrm{marbles}\:\mathrm{will}\:\mathrm{be}\:\mathrm{red}\:\mathrm{if}\:\mathrm{3}\:\mathrm{marbles} \\ $$$$\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{without}\:\mathrm{replacement} \\ $$ Commented by mr W last…
Question Number 76954 by behi83417@gmail.com last updated on 01/Jan/20 $$\int\:\:\:\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt{\mathrm{1}+\boldsymbol{\mathrm{sinx}}.\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}}}\:\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com