Question Number 97892 by pranesh last updated on 10/Jun/20 Answered by john santu last updated on 10/Jun/20 $$\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x} \\ $$$$\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x}+\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}\:\mathrm{4x} \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}\:\mathrm{4x} \\…
Question Number 32354 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{sin}^{\mathrm{2}} {t}\right)^{\mathrm{2}} }\:. \\ $$ Commented by abdo imad last updated on 28/Mar/18…
Question Number 32352 by abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left(\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right){dx} \\ $$ Commented by abdo imad last updated on 26/Mar/18 $${ch}.{x}={sint}\:\Rightarrow\:{I}\:=\:\int_{\mathrm{0}}…
Question Number 32353 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}\left({x}\right){ln}\left({cos}\left({x}\right)\right){dx}\:. \\ $$ Answered by sma3l2996 last updated on 25/Mar/18 $${A}=\int_{\mathrm{0}} ^{\pi/\mathrm{4}} {cos}\left({x}\right){ln}\left({cosx}\right){dx}…
Question Number 32350 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32351 by abdo imad last updated on 23/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\:\frac{{dt}}{\mathrm{1}+{cos}\theta\:{sint}}\:.\: \\ $$ Answered by sma3l2996 last updated on 25/Mar/18 $${let}\:{x}={tan}\left({t}/\mathrm{2}\right)\Rightarrow{dt}=\frac{\mathrm{2}{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\…
Question Number 32349 by abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{xdx}}{\mathrm{1}+{sinx}}\:. \\ $$ Commented by abdo imad last updated on 24/Mar/18 $${the}\:{ch}.{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\…
Question Number 32342 by abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\int\int_{{D}} \:\:\:\frac{{dxdy}}{\left(\mathrm{4}{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$${D}=\left\{\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:/\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\:{and}\:{y}\:\leqslant\mathrm{2}{x}\:\right\}\:. \\ $$ Terms of Service…
Question Number 32343 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{{dt}}{{x}−{e}^{{it}} }\:\:. \\ $$ Commented by abdo imad last updated on 28/Mar/18 $${let}\:{put}\:{I}\left({x}\right)\:=\:\int_{\mathrm{0}}…
Question Number 163414 by AbdullahIbrahim last updated on 06/Jan/22 $$\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{cosx}}\:\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}}+\sqrt{\boldsymbol{{sinx}}\:\boldsymbol{{cos}}^{\mathrm{3}} \boldsymbol{{x}}}} \\ $$ Answered by Ar Brandon last updated on 06/Jan/22 $${I}=\int\frac{{dx}}{\:\sqrt{\mathrm{cos}{x}\mathrm{sin}^{\mathrm{3}} {x}}+\sqrt{\mathrm{sin}{x}\mathrm{cos}^{\mathrm{3}} {x}}}…