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Category: Integration

find-pi-4-pi-4-cosx-2-5sinx-dx-

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} \\…

let-f-x-0-1-dt-1-x-1-t-2-with-x-gt-0-1-detemine-a-explicit-form-of-f-x-2-find-also-g-x-0-1-1-t-2-1-x-1-t-2-2-dt-3-find-the-value-of-integrals-0-1-dt-

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} \\…

let-A-n-0-pi-2-cos-n-xdx-1-calculate-A-0-A-2-and-A-3-2-calculate-A-n-interms-of-n-3-find-0-pi-2-cos-8-xdx-

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}}…

let-X-n-0-pi-4-sin-n-xdx-1-calculate-X-0-X-1-X-2-X-3-2-find-X-n-interms-of-n-3-find-the-value-of-0-pi-4-sin-8-xdx-

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} \\…

let-f-x-0-dt-t-4-x-4-with-x-gt-0-1-determine-a-explicit-form-of-f-x-2-find-also-g-x-0-dt-t-4-x-4-2-3-give-f-n-x-at-form-of-integral-4-calculate-0-

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}} }…