Question Number 48829 by Ali Yousafzai last updated on 29/Nov/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int\mathrm{1}^{{x}} \left[{t}^{\mathrm{2}} \left({e}^{\mathrm{1}/{t}} −\mathrm{1}\right)−{t}\right]{dt}}{{x}^{\mathrm{2}} \mathrm{ln}\:\left(\mathrm{1}+\mathrm{1}/{x}\right)} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18…
Question Number 114330 by mnjuly1970 last updated on 18/Sep/20 Commented by mnjuly1970 last updated on 18/Sep/20 $${easy}\:{question}\uparrow\uparrow\uparrow \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 179862 by cherokeesay last updated on 03/Nov/22 Commented by CElcedricjunior last updated on 03/Nov/22 $$\begin{cases}{\boldsymbol{{y}}=\boldsymbol{{lnx}}}\\{\boldsymbol{{y}}=\mathrm{2}}\end{cases}=>\boldsymbol{{lnx}}=\mathrm{2}=>\boldsymbol{{x}}=\boldsymbol{{e}}^{\mathrm{2}} \\ $$$$\left.=\left.>\boldsymbol{{x}}\in\right]\mathrm{0};\boldsymbol{{e}}^{\mathrm{2}} \right]\:\boldsymbol{{et}}\:\boldsymbol{{y}}\in\left[\boldsymbol{{lnx}};\mathrm{2}\right] \\ $$$$\Leftrightarrow\boldsymbol{{A}}=\int_{\boldsymbol{{lnx}}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\boldsymbol{{e}}^{\mathrm{2}}…
Question Number 179853 by AKSHAYTHAKUR last updated on 03/Nov/22 $$\int\frac{\boldsymbol{{xdx}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)} \\ $$ Commented by CElcedricjunior last updated on 04/Nov/22 $$\int\:\frac{\boldsymbol{{xdx}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)}=\int\left[\frac{\mathrm{1}}{\boldsymbol{{x}}−\mathrm{2}}+\frac{\mathrm{1}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)}\right]\boldsymbol{{dx}} \\ $$$$={ln}\mid\boldsymbol{{x}}−\mathrm{2}\mid+\int\left[−\frac{\mathrm{1}}{\boldsymbol{{x}}−\mathrm{1}}+\frac{\mathrm{1}}{\boldsymbol{{x}}−\mathrm{2}}\right]\boldsymbol{{dx}} \\ $$$$=\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{2}\mid−\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{1}\mid+\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{1}\mid \\…
Question Number 114320 by mnjuly1970 last updated on 18/Sep/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 179852 by arup last updated on 03/Nov/22 $$\boldsymbol{{prove}}\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{{log}}\left(\boldsymbol{{sinx}}\right)\boldsymbol{{dx}}=\frac{\pi}{\mathrm{2}}\boldsymbol{{log}}\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by som(math1967) last updated on 03/Nov/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {log}\left[{sin}\left(\frac{\pi}{\mathrm{2}}−{x}\right)\right]{dx} \\…
Question Number 179844 by mathlove last updated on 03/Nov/22 $$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right){lnx}}{dx}=? \\ $$ Answered by Peace last updated on 03/Nov/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}−{x}^{{s}} }{\left({x}+\mathrm{1}\right){ln}\left({x}\right)}={f}\left({s}\right)…
Question Number 114302 by mnjuly1970 last updated on 18/Sep/20 $$\:\:\:\:\:\:\:\:….\:{calculus}\:…. \\ $$$$\:\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${i}::\int_{\mathrm{0}} ^{\:\mathrm{1}} {t}^{\mathrm{2}} {ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right){dt}=??? \\ $$$${ii}:::\:\psi^{'} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)=??? \\ $$$${iii}:::\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{8}}}…
Question Number 48757 by sandeepkeshari0797@gmail.com last updated on 28/Nov/18 Commented by maxmathsup by imad last updated on 28/Nov/18 $${method}\:{with}\:{one}\:{parametr}\:{let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sint}}{{t}}\:{e}^{−{tx}} {dt}\:{with}\:{x}\geqslant\mathrm{0}\:{we}\:{have} \\ $$$${f}^{'} \left({x}\right)=−\int_{\mathrm{0}}…
Question Number 48725 by Tawa1 last updated on 27/Nov/18 $$\int\:\int\:\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\:\:\:\mathrm{dx}\:\mathrm{dy},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{3y}}\:\:\:\leqslant\:\:\mathrm{x}\:\:\leqslant\:\:\sqrt{\mathrm{4}\:−\:\mathrm{y}^{\mathrm{2}} }\:\:,\:\:\:\:\:\:\:\:\:\mathrm{0}\:\leqslant\:\mathrm{y}\:\leqslant\:\mathrm{2} \\ $$ Commented by Abdo msup. last updated on 27/Nov/18 $${let}\:{I}\:=\int\int_{{D}} \:\:\sqrt{{x}^{\mathrm{2}}…