Question Number 118674 by mathace last updated on 19/Oct/20 $${Please}\:{integrate} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}+{x}^{{c}} }{dx}\:{where}\:{c}\:{is}\:{a}\:{constant}. \\ $$ Answered by Dwaipayan Shikari last updated on 19/Oct/20…
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…
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…
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 $${i}\:{am}\:{using}\:{simple}\:{logic}.. \\…
Question Number 53114 by maxmathsup by imad last updated on 17/Jan/19 $${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…
Question Number 53113 by maxmathsup by imad last updated on 17/Jan/19 $${let}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{t}+\mathrm{1}}{\left({t}^{\mathrm{2}} −{t}+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$$${find}\:{value}\:{of}\:{I}\:. \\ $$ Commented by maxmathsup by imad…
Question Number 53112 by maxmathsup by imad last updated on 21/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{1}+\mathrm{2}{sinx}}{\mathrm{3}\:+\mathrm{2}{cosx}}{dx} \\ $$$${let}\:{A}\:=\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{1}+\mathrm{2}{sinx}}{\mathrm{3}\:+\mathrm{2}{cosx}}{dx}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${A}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}+\frac{\mathrm{4}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{3}+\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}\:\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 53089 by Tawa1 last updated on 17/Jan/19 $$\int_{\:\frac{\pi}{\mathrm{2}}\:} ^{\:\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{5}\:+\:\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{tanh}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{3}}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 53080 by Abdo msup. last updated on 17/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{cos}^{\mathrm{2}} {x}}{\mathrm{2}+\mathrm{3}{sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$ Commented by maxmathsup by imad last updated on 17/Jan/19…
Question Number 53081 by cesar.marval.larez@gmail.com last updated on 17/Jan/19 Answered by tanmay.chaudhury50@gmail.com last updated on 17/Jan/19 $$\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}}…