Question Number 65776 by mathmax by abdo last updated on 03/Aug/19 $${find}\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{cosx}}{\mathrm{2}+\mathrm{5}{sinx}}{dx} \\ $$ Commented by kaivan.ahmadi last updated on 04/Aug/19 $${u}=\mathrm{2}+\mathrm{5}{sinx}\Rightarrow{du}=\mathrm{5}{cosxdx} \\…
Question Number 65774 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\frac{{sin}^{\mathrm{2}} {x}}{{sin}^{\mathrm{2}} \left(\frac{{nx}}{\mathrm{2}}\right)}{dx}\:\:\:\:\left({n}>\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 65773 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+{x}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){detemine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}{\left(\mathrm{1}+{x}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\right)^{\mathrm{2}} }{dt} \\…
Question Number 65775 by mathmax by abdo last updated on 03/Aug/19 $$\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{tanx}}{\mathrm{2}+\mathrm{3}{cosx}}{dx} \\ $$ Commented by mathmax by abdo last updated on 04/Aug/19…
Question Number 65770 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int_{\mathrm{0}}…
Question Number 65769 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{2}{xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by ~ À ® @ 237…
Question Number 65768 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 65771 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{X}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{X}_{\mathrm{0}} \:,{X}_{\mathrm{1}} \:,{X}_{\mathrm{2}} ,{X}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{X}_{{n}} {interms}\:{of}\:{n} \\…
Question Number 65767 by mathmax by abdo last updated on 03/Aug/19 $${let}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{4}} +{x}^{\mathrm{4}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} }…
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