Question Number 89343 by Ar Brandon last updated on 17/Apr/20 $${Given}\:\alpha\:{and}\:\beta\:\in\mathbb{N}\:{such}\:{that} \\ $$$${I}\left(\alpha,\beta\right)=\int_{} ^{\mathrm{1}} {t}^{\alpha} \left(\mathrm{1}−{t}\right)^{\beta} {dt} \\ $$$${show}\:{that} \\ $$$${I}\left(\alpha;\beta\right)=\frac{\alpha!\beta!}{\left(\alpha+\beta+\mathrm{1}\right)!} \\ $$ Commented by…
Question Number 89341 by Henri Boucatchou last updated on 17/Apr/20 $$\underset{{n}\rightarrow\infty} {{lim}}\sqrt[{{n}}]{\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}{sin}\left(\frac{{k}\pi}{\mathrm{2}{n}}\right)}=? \\ $$ Commented by Henri Boucatchou last updated on 17/Apr/20 $$\boldsymbol{{Check}}\:\:\boldsymbol{{once}}\:\:\boldsymbol{{more}}\:\:\boldsymbol{{Sir}},\:\:\:\boldsymbol{{ln}}\underset{{i}}…
Question Number 154872 by talminator2856791 last updated on 22/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \mathrm{sin}\left({x}^{\mathrm{3}} \right)\mathrm{cos}\left({x}^{\mathrm{4}} \right){dx} \\ $$$$\: \\ $$ Answered by mnjuly1970 last updated…
Question Number 154875 by mathdanisur last updated on 22/Sep/21 Answered by mindispower last updated on 23/Sep/21 $${u}={log}\left({x}+\frac{\mathrm{5}}{{x}}\right) \\ $$$$\Omega\Leftrightarrow\int{e}^{\mathrm{2}{u}} {sin}\left({u}\right){du} \\ $$ Commented by mathdanisur…
Question Number 23796 by tapan das last updated on 06/Nov/17 $$\int\frac{\mathrm{2sinx}+\mathrm{3cosx}}{\mathrm{3sinx}+\mathrm{4cosx}}\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 06/Nov/17 $$\mathrm{2sin}\:{x}+\mathrm{3cos}\:{x}={A}\left(\mathrm{3sin}\:{x}+\mathrm{4cos}\:{x}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+{B}\left(\mathrm{3cos}\:{x}−\mathrm{4sin}\:{x}\right) \\ $$$$\Rightarrow\:\mathrm{3}{A}−\mathrm{4}{B}=\mathrm{2}\:\:{and}…
Question Number 23793 by math solver last updated on 06/Nov/17 Commented by math solver last updated on 06/Nov/17 $$\mathrm{q}.\mathrm{2},\mathrm{3} \\ $$ Answered by ajfour last…
Question Number 154860 by Jamshidbek last updated on 22/Sep/21 $$\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{3}}+…+\frac{\mathrm{1}}{\mathrm{2n}}<\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{n}>\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89327 by Ar Brandon last updated on 16/Apr/20 Commented by MJS last updated on 16/Apr/20 $$\mathrm{look}\:\mathrm{at}\:\mathrm{qu}.\:\mathrm{89290} \\ $$ Commented by Ar Brandon last…
Question Number 89324 by 174 last updated on 16/Apr/20 Commented by mathmax by abdo last updated on 16/Apr/20 $$\:\:{let}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({a}+{cos}^{\mathrm{2}} {x}\right){dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${f}^{'} \left({a}\right)\:=\int_{\mathrm{0}}…
Question Number 154857 by CAIMAN last updated on 22/Sep/21 Answered by mindispower last updated on 23/Sep/21 $${ln}\left({ch}\left(\right)+{cos}\left(…..\right)\right){dx}? \\ $$ Terms of Service Privacy Policy Contact:…