Question Number 48494 by maxmathsup by imad last updated on 24/Nov/18 $${find}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}−{cos}\left({n}+\mathrm{1}\right){x}}{\mathrm{2}{sin}\left(\frac{{x}}{\mathrm{2}}\right)}{dx}\:. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Nov/18 $${A}_{{n}}…
Question Number 48491 by maxmathsup by imad last updated on 24/Nov/18 $${prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(\mathrm{1}+{t}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} −\left(\mathrm{1}+{t}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} }{{t}}{dt}\:{is}\:{convergent}\:{and}\:{find}\:{its}\:{value}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 48484 by Meritguide1234 last updated on 24/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 24/Nov/18 $${trying}\:{to}\:{solve} \\ $$$${let}\:{in}\:{place}\:{of}\:\sqrt{\mathrm{3}}\:\:{putting}\:\:{a}\:\:\:\:\:{a}=\sqrt{\mathrm{3}}\: \\ $$$${finding}\:{the}\:{values}\:{of}\:{x}\:\:{so}\:{that} \\ $$$${sinax}={sinx} \\ $$$${ax}={k}\pi+\left(−\mathrm{1}\right)^{{k}}…
Question Number 179513 by cortano1 last updated on 30/Oct/22 $$\:\mathrm{F}\left(\mathrm{x}\right)\:=\:\int\:\frac{\mathrm{1}}{\mathrm{x}}\:\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\:\:\mathrm{F}\left(\mathrm{1}\right)=\mathrm{0}\: \\ $$$$\:\:\mathrm{F}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=? \\ $$ Answered by mr W last updated on 30/Oct/22 $${let}\:{t}=\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}…
Question Number 179510 by Acem last updated on 30/Oct/22 $${Evaluate}\:\int{e}^{\mathrm{4}{x}} \:\sqrt{\frac{\mathrm{1}}{{e}^{−\mathrm{2}{x}} }+\mathrm{1}}\:{dx} \\ $$ Commented by cortano1 last updated on 30/Oct/22 $$\sqrt{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}}\:=\:\lambda\:\Rightarrow\mathrm{e}^{\mathrm{2x}} =\lambda^{\mathrm{2}} −\mathrm{1}…
Question Number 179511 by Acem last updated on 30/Oct/22 $${Evaluate}\:\int\frac{{x}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{7}}}\:{dx} \\ $$ Answered by ARUNG_Brandon_MBU last updated on 30/Oct/22 $$=\frac{\mathrm{1}}{\mathrm{4}}\int\frac{\mathrm{4}{x}−\mathrm{4}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{7}}}{dx}+\int\frac{{dx}}{\:\sqrt{\mathrm{2}\left({x}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{9}}} \\ $$$$=\frac{\sqrt{\mathrm{2}{x}^{\mathrm{2}}…
Question Number 179478 by Acem last updated on 29/Oct/22 $${Find}\:\int_{\:\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{6}}} \:\frac{\mathrm{1}}{{x}^{−\mathrm{5}} \:\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:{dx} \\ $$ Answered by MJS_new last updated on 29/Oct/22 $$\int\frac{{dx}}{{x}^{−\mathrm{5}}…
Question Number 113929 by gloriousman last updated on 16/Sep/20 $$\int\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{5}} \mathrm{dx}\: \\ $$$$ \\ $$ Commented by ShakaLaka last updated on 16/Sep/20 $${we}\:{can}\:{also}\:{solve}\:{by}\:{simplification} \\…
Question Number 113910 by bobhans last updated on 16/Sep/20 $$\left(\mathrm{1}\right)\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{4}} {x}}{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{{x}}\right)}}{\frac{\mathrm{1}}{{x}}}\:? \\ $$ Answered by bemath last updated on…
Question Number 113907 by bemath last updated on 16/Sep/20 $$\int\:\sqrt{{x}}\:\mathrm{cos}\:\left(\sqrt{{x}}\right)\:{dx} \\ $$ Answered by bobhans last updated on 16/Sep/20 $${K}=\int\:\sqrt{{x}}\:\mathrm{cos}\:\left(\sqrt{{x}}\right)\:{dx}\: \\ $$$${let}\:{x}={t}^{\mathrm{2}} \:\Rightarrow{dx}\:=\:\mathrm{2}{t}\:{dt}\: \\ $$$${K}=\:\int\:\mathrm{2}{t}^{\mathrm{2}}…