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Category: Integration

Given-f-x-0-x-dt-f-t-2-and-0-2-dt-f-t-2-6-1-3-Then-then-the-value-of-f-9-is-

Question Number 118663 by benjo_mathlover last updated on 19/Oct/20 $$\:{Given}\:{f}\left({x}\right)\:=\:\int\:\underset{\mathrm{0}} {\overset{{x}} {\:}}\:\frac{{dt}}{\left[{f}\left({t}\right)\right]^{\mathrm{2}} }\:\:{and}\:\int\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\:}}\:\frac{{dt}}{\left[\:{f}\left({t}\right)\right]^{\mathrm{2}} }\:=\:\sqrt[{\mathrm{3}\:}]{\mathrm{6}}\: \\ $$$${Then}\:{then}\:{the}\:{value}\:{of}\:{f}\left(\mathrm{9}\right)\:{is}\:\_\_ \\ $$ Commented by mr W last…

Evaluate-1-2-x-4-x-dx-2-x-2-x-4-dx-3-x-2-x-4-dx-4-dx-2sinx-3secx-

Question Number 53119 by rahul 19 last updated on 18/Jan/19 $${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right)\:\int\sqrt{\frac{\mathrm{2}−{x}}{\mathrm{4}+{x}}}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:\int\:\sqrt{\frac{{x}−\mathrm{2}}{{x}−\mathrm{4}}}\:{dx} \\ $$$$\left.\mathrm{3}\right)\:\int\:\sqrt{\left({x}−\mathrm{2}\right)\left({x}−\mathrm{4}\right)}\:{dx} \\ $$$$\left.\mathrm{4}\right)\:\int\:\frac{{dx}}{\mathrm{2sin}\boldsymbol{{x}}+\mathrm{3sec}\boldsymbol{{x}}}\:. \\ $$ Commented by maxmathsup by…

If-a-lt-0-2pi-1-10-3-cos-x-dx-lt-b-then-the-ordered-pair-a-b-is-

Question Number 53118 by gunawan last updated on 18/Jan/19 $$\mathrm{If}\:{a}<\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{\mathrm{1}}{\mathrm{10}+\mathrm{3}\:\mathrm{cos}\:{x}}\:{dx}<{b},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{ordered}\:\mathrm{pair}\:\left({a},\:{b}\right)\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 18/Jan/19 $${i}\:{am}\:{using}\:{simple}\:{logic}.. \\…

let-A-n-0-x-sin-nx-x-2-n-2-2-dx-with-n-integr-natural-not-0-1-find-the-value-of-A-n-2-study-the-convergence-of-A-n-

Question Number 53114 by maxmathsup by imad last updated on 17/Jan/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}\:{sin}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr}\:{natural}\:{not}\:\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{A}_{{n}} \\ $$ Commented…

calculate-0-pi-1-2sinx-3-2cosx-dx-let-A-0-pi-1-2sinx-3-2cosx-dx-changement-tan-x-2-t-give-A-0-1-4t-1-t-2-3-2-1-t-2-1-t-2-2dt-1-t-2-2-0-

Question Number 53112 by maxmathsup by imad last updated on 21/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{1}+\mathrm{2}{sinx}}{\mathrm{3}\:+\mathrm{2}{cosx}}{dx} \\ $$$${let}\:{A}\:=\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{1}+\mathrm{2}{sinx}}{\mathrm{3}\:+\mathrm{2}{cosx}}{dx}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${A}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}+\frac{\mathrm{4}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{3}+\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}\:\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}}…

Question-53081

Question Number 53081 by cesar.marval.larez@gmail.com last updated on 17/Jan/19 Answered by tanmay.chaudhury50@gmail.com last updated on 17/Jan/19 $$\left.\mathrm{1}\right)\int{e}^{\mathrm{2}{x}} {sinxdx} \\ $$$${e}^{\mathrm{2}{x}} \int{sinxdx}−\int\left[\frac{{d}\left({e}^{\mathrm{2}{x}} \right)}{{dx}}\int{sinxdx}\right]{dx} \\ $$$$={e}^{\mathrm{2}{x}} ×−{cosx}−\int\mathrm{2}{e}^{\mathrm{2}{x}}…