Question Number 51526 by ajfour last updated on 27/Dec/18 Commented by ajfour last updated on 27/Dec/18 $${For}\:{the}\:{area}\:{in}\:{black}\:{and}\:{yellow} \\ $$$${to}\:{be}\:{the}\:{same},\:{find}\:{r}\:{in}\:{terms}\:{of}\:{R}. \\ $$$$ \\ $$ Answered by…
Question Number 117053 by bemath last updated on 09/Oct/20 $$\:\:\:\int\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=? \\ $$ Answered by Lordose last updated on 09/Oct/20 $$\mathrm{u}=\mathrm{x}^{\mathrm{2}} \:\Rightarrow\:\mathrm{du}=\mathrm{2xdx} \\ $$$$\mathrm{I}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}−\mathrm{u}^{\mathrm{2}} }}\mathrm{du}…
Question Number 51510 by Tinkutara last updated on 27/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 28/Dec/18 $$\int\frac{−\mathrm{2}{pdp}}{\:\sqrt{{p}^{\mathrm{2}} ×\left(\left\{\mathrm{1}−\mathrm{3}\left({p}^{\mathrm{2}} −\mathrm{1}\right)\right\}\right.}} \\ $$$${x}^{\mathrm{2}} \left\{{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\mathrm{2}\left({x}+\frac{\mathrm{1}}{{x}}\right)−\mathrm{1}\right\} \\…
Question Number 51501 by Tinkutara last updated on 27/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18 $${x}={tan}\theta\:\:{dx}={sec}^{\mathrm{2}} \theta{d}\theta \\ $$$$\int\frac{\theta}{{tan}^{\mathrm{4}} \theta}{sec}^{\mathrm{2}} \theta{d}\theta \\ $$$$\theta\int\frac{{sec}^{\mathrm{2}} \theta}{{tan}^{\mathrm{4}}…
Question Number 117034 by Lordose last updated on 09/Oct/20 $$\int\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{3}} }} \\ $$ Answered by MJS_new last updated on 09/Oct/20 $$\int\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{1}}}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{1}}}{{x}}\:\rightarrow\:{dx}=−{x}^{\mathrm{2}}…
Question Number 117006 by TANMAY PANACEA last updated on 08/Oct/20 $$\int_{\mathrm{0}} ^{\mathrm{100}\pi} \mid{sinx}\mid\:{dx} \\ $$ Commented by TANMAY PANACEA last updated on 08/Oct/20 $${thank}\:{you}\:{sir} \\…
Question Number 117002 by TANMAY PANACEA last updated on 08/Oct/20 $$\int_{\mathrm{0}} ^{{n}\pi+{v}} \mid{sinx}\mid\:{dx} \\ $$ Answered by TANMAY PANACEA last updated on 08/Oct/20 $$\mid{sinx}\mid\:{is}\:{alsays}\:+{ve}\:{and}\:{each}\:{loop}\:{area}\:{of} \\…
Question Number 116998 by TANMAY PANACEA last updated on 08/Oct/20 $$\int_{\frac{−\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{2}^{{x}} }{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 08/Oct/20…
Question Number 116999 by TANMAY PANACEA last updated on 08/Oct/20 $$\int\frac{{dx}}{\left({a}+{bcosx}\right)^{\mathrm{2}} } \\ $$ Answered by Olaf last updated on 08/Oct/20 $$\mathrm{I}\left({x}\right)\:=\:\int\frac{{dx}}{\left({a}+{b}\frac{{e}^{{ix}} +{e}^{−{ix}} }{\mathrm{2}}\right)^{\mathrm{2}} }…
Question Number 116996 by mnjuly1970 last updated on 08/Oct/20 Answered by mindispower last updated on 09/Oct/20 $${the}\:{last}\:{is}\:{li}_{\mathrm{3}} \left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right)\int? \\ $$ Commented by mnjuly1970 last updated…