Question Number 137191 by Dwaipayan Shikari last updated on 30/Mar/21 $${Some}\:{useful}\:{approximations}\:{of}\:{sine}\:{function} \\ $$$${sin}\left(\frac{\pi}{\mathrm{7}}\right)=\frac{\mathrm{96}}{\mathrm{221}} \\ $$$${sin}\left(\frac{\pi}{\mathrm{9}}\right)=\frac{\mathrm{128}}{\mathrm{373}} \\ $$$${sin}\left(\frac{\pi}{\mathrm{11}}\right)=\frac{\mathrm{32}}{\mathrm{113}} \\ $$$$… \\ $$$${I}\:{am}\:{counting}\:{more}\:..{thanking}\:{you}! \\ $$ Terms of…
Question Number 137190 by mnjuly1970 last updated on 30/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}\:…….\:\:{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:{prove}\:{that}::: \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left({ln}\left(\frac{\mathrm{1}}{{x}}\right)\right).\frac{{dx}}{\:\sqrt{{ln}\left(\frac{\mathrm{1}}{{x}}\right)}}\:=−\sqrt{\pi}\:\left(\gamma+{ln}\left(\mathrm{4}\right)\right) \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last…
Question Number 6116 by sanusihammed last updated on 14/Jun/16 $${Integrate}\:\:\:\left[\mathrm{1}\:+\:\left({tanx}\right)^{{a}} \right]^{−\mathrm{1}} \:\:{dx} \\ $$$$ \\ $$$${For}\:\:\mathrm{0}\:<\:{x}\:<\:\:\Pi/\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137185 by metamorfose last updated on 30/Mar/21 $$\int_{\mathrm{1}} ^{{x}} {e}^{\left(\mathrm{1}−{ln}^{\mathrm{2}} {t}\right)^{\frac{\mathrm{1}}{{n}}} } {dt}=…?\:{n}\:{an}\:{integer} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6115 by Rasheed Soomro last updated on 14/Jun/16 $${Solve}\:{the}\:{system}\:{of}\:{following}\:{equations} \\ $$$${a}^{\mathrm{3}} −{bcd}=−\mathrm{32} \\ $$$${b}^{\mathrm{3}} −{acd}=−\mathrm{79} \\ $$$${c}^{\mathrm{3}} −{abd}=\mathrm{109} \\ $$$${d}^{\mathrm{3}} −{abc}=\mathrm{502} \\ $$…
Question Number 137187 by mathocean1 last updated on 30/Mar/21 $${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sin}^{{n}} {x}\:{dx} \\ $$$${Write}\:{a}\:{relation}\:{between}\:{I}_{{n}+\mathrm{2}} \:{and}\:{I}_{{n}} . \\ $$ Answered by Dwaipayan Shikari last…
Question Number 6113 by enigmeyou last updated on 14/Jun/16 $$\int_{\mathrm{0}} ^{\mathrm{100}} {E}\left({x}\right){dx}=? \\ $$$$ \\ $$ Commented by 123456 last updated on 14/Jun/16 $$\mathrm{what}\:\mathrm{is}\:\mathrm{E}\left({x}\right)? \\…
Question Number 71649 by TawaTawa last updated on 18/Oct/19 Commented by mathmax by abdo last updated on 18/Oct/19 $$\sum_{{n}=\mathrm{1}} ^{\left[{x}\right]} \sqrt{{n}}=\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+…+\sqrt{\left[{x}\right]} \\ $$$$\frac{\mathrm{2}}{\mathrm{3}}\sqrt{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{3}} }=\frac{\mathrm{2}}{\mathrm{3}}\sqrt{{x}^{\mathrm{3}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{3}}…
Question Number 6111 by Kasih last updated on 14/Jun/16 $${log}^{\mathrm{2}} {x}+{logx}^{\mathrm{2}} −\mathrm{3}=\mathrm{0}\:,\:{x}=? \\ $$ Answered by prakash jain last updated on 14/Jun/16 $$\mathrm{log}\:{x}={u} \\ $$$${u}^{\mathrm{2}}…
Question Number 71645 by ajfour last updated on 18/Oct/19 Commented by ajfour last updated on 18/Oct/19 $${If}\:{the}\:{three}\:{inner}\:{solid}\:{spheres} \\ $$$${have}\:{radii}\:{p},{q},{r}\:{and}\:{the}\:{same}\: \\ $$$${density}\:\rho,\:{while}\:{the}\:{outer}\:{sphere} \\ $$$${has}\:{radius}\:{R},\:{and}\:{negligible} \\ $$$${mass},\:{find}\:{how}\:{high}\:{from}\:{ground}…