Question Number 48498 by maxmathsup by imad last updated on 24/Nov/18 $${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}^{{n}} {xdx}\:\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}^{\mathrm{6}} {xdx}\:{and}\:\int_{\mathrm{0}}…
Question Number 48497 by maxmathsup by imad last updated on 24/Nov/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{xplicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\: \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 48496 by maxmathsup by imad last updated on 24/Nov/18 $${find}\:{f}\left({x}\right)\:=\int\:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 48495 by maxmathsup by imad last updated on 24/Nov/18 $$\left.\mathrm{1}\right){calculate}\:\:{I}\:=\int\:\frac{{ln}\left(\mathrm{1}+{t}\right)}{\mathrm{1}+{t}}{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{t}\right)}{\mathrm{1}+{t}}{dt} \\ $$ Commented by maxmathsup by imad last updated…
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}}…