Question Number 44473 by abdo.msup.com last updated on 29/Sep/18 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{sin}\left({n}\left[{t}\right]\right){e}^{−{t}} {dt} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}} \:\:{and}\:{lim}_{{n}\rightarrow+\infty} {n}\:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{convergence}\:{of}\:\sum_{{n}} \:{A}_{{n}} \\ $$ Commented by…
Question Number 44470 by abdo.msup.com last updated on 29/Sep/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} {sin}^{\mathrm{2}} {t}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 44471 by abdo.msup.com last updated on 29/Sep/18 $${calculste}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left({x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on 30/Sep/18 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 175531 by cortano1 last updated on 01/Sep/22 $$\:\int\:\frac{{dt}}{\mathrm{5cos}\:{t}+\mathrm{6sin}\:{t}}\:=? \\ $$ Answered by Ar Brandon last updated on 01/Sep/22 $${I}=\int\frac{{dt}}{\mathrm{5cos}{t}+\mathrm{6sin}{t}}\:,\:{x}=\mathrm{tan}\frac{{t}}{\mathrm{2}} \\ $$$$\:\:\:=\int\frac{\mathrm{2}}{\mathrm{5}\left(\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }\right)+\mathrm{6}\left(\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 44466 by maxmathsup by imad last updated on 29/Sep/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}\:{sinx}}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{4}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{xsinx}}{\left({a}^{\mathrm{2}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} }{dx}…
Question Number 109989 by 150505R last updated on 26/Aug/20 Commented by 150505R last updated on 26/Aug/20 $${please}\:{solve} \\ $$ Answered by maths mind last updated…
Question Number 109988 by 150505R last updated on 26/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 44441 by Tawa1 last updated on 29/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18 $$\underset{{t}\rightarrow\mathrm{0}\:} {\mathrm{lim}}\:\frac{{e}^{−\mathrm{5}{t}} −\mathrm{1}}{−\mathrm{5}{t}}×−\mathrm{5} \\ $$$$=\mathrm{1}×−\mathrm{5}=−\mathrm{5} \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{t}^{\mathrm{11}} }{{t}^{\mathrm{11}}…
Question Number 44424 by peter frank last updated on 28/Sep/18 $${by}\:{considering}\:\:{a}\:{sermicircle}\:{from}\:−{r}\:{to}\:\:{r}\:{prove}\:{that}\:{area}\:{of}\:{circle}\:{is}\:\pi{r}^{\mathrm{2}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18 $$\mathrm{2}\int_{−{r}} ^{{r}} \sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }\:\:{dx}…
Question Number 44422 by peter frank last updated on 28/Sep/18 $${use}\:{substitution}\:{x}=\mathrm{cos}\:^{\mathrm{2}} \theta+\mathrm{3}{sin}^{\mathrm{2}} \theta \\ $$$${show}\:{that}\int_{\mathrm{1}} ^{\mathrm{3}} \frac{{dx}}{\:\sqrt{\left({x}−\mathrm{1}\right)\left(\mathrm{3}−{x}\right)}}=\pi \\ $$ Commented by maxmathsup by imad last…