Question Number 133538 by mathmax by abdo last updated on 22/Feb/21 $$\mathrm{calculate}\:\int\int_{\left[\mathrm{1},\mathrm{2}\right]^{\mathrm{2}} } \:\:\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{3y}^{\mathrm{2}} }\mathrm{e}^{−\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3y}^{\mathrm{2}} \right)} \mathrm{dxdy} \\ $$ Terms of Service Privacy…
Question Number 133533 by Raxreedoroid last updated on 22/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{that}\:\mathrm{is}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curves} \\ $$$${y}={x}^{\mathrm{3}} ,{y}=\mathrm{8},{x}=\mathrm{0},\:\mathrm{rotated}\:\mathrm{about}\:{x}=\mathrm{9} \\ $$ Answered by bemath last updated on 23/Feb/21 $$\mathrm{V}=\pi\underset{\mathrm{0}} {\overset{\mathrm{8}} {\int}}\left(\mathrm{9}−\sqrt[{\mathrm{3}}]{\mathrm{y}}\:\right)^{\mathrm{2}}…
Question Number 133530 by snipers237 last updated on 22/Feb/21 $$\:{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(−{lnx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\: \\ $$ Commented by Dwaipayan Shikari last updated on 22/Feb/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 2435 by Yozzi last updated on 20/Nov/15 $${Prove}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Gamma'\left(\mathrm{1}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {lnxdx} \\ $$$${is}\:{a}\:{negative}\:{number}. \\ $$ Commented by prakash jain last updated…
Question Number 2434 by Yozzi last updated on 20/Nov/15 $${Prove}\:{that}\:{for}\:{m}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow−{m}} {\mathrm{lim}}\Gamma\left({x}\right)=\infty. \\ $$ Answered by 123456 last updated on 25/Nov/15 $$\Gamma\left({x}+\mathrm{1}\right)={x}\Gamma\left({x}\right) \\ $$$$\mathrm{so}…
Question Number 67963 by mhmd last updated on 02/Sep/19 Commented by mathmax by abdo last updated on 02/Sep/19 $${generally}\:{if}\:{F}\left({x}\right)=\int_{{u}\left({x}\right)} ^{{v}\left({x}\right)} {f}\left({t}\right){dt}\:\Rightarrow{F}^{'} \left({x}\right)={v}^{'} \left({x}\right){f}\left({v}\left({x}\right)\right)−{u}^{'} \left({x}\right){f}\left({u}\left({x}\right)\right) \\…
Question Number 67959 by mhmd last updated on 02/Sep/19 $$\int\sqrt{{e}^{{y}^{\mathrm{2}} } \:\:}\:{dy}\:\:{pleas}\:{sir}\:{can}\:{you}\:{help}\:{me}? \\ $$ Commented by Prithwish sen last updated on 02/Sep/19 $$\mathrm{please}\:\mathrm{check}\:\mathrm{Q67942}\:\mathrm{it}\:\mathrm{has}\:\mathrm{been}\:\mathrm{done} \\ $$…
Question Number 133490 by mnjuly1970 last updated on 22/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{advnced}\:\:{calculus}…. \\ $$$$\:\:\:\:{prove}:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({tan}\left({x}\right)\right)}{{x}}{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\frac{\mathrm{1}}{{e}}\right) \\ $$$$\:{prove}\:{that}:\:\boldsymbol{\Phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx}=\sqrt{\pi} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:…
Question Number 67942 by mhmd last updated on 02/Sep/19 $$\int{e}^{{y}^{\mathrm{2}} /\mathrm{2}} \:\:{dy} \\ $$ Commented by mr W last updated on 09/Feb/21 $$\int{e}^{\frac{{y}^{\mathrm{2}} }{\mathrm{2}}} {dy}=\sqrt{\frac{\pi}{\mathrm{2}}}\:{erfi}\left(\frac{{y}}{\:\sqrt{\mathrm{2}}}\right)+{C}…
Question Number 67937 by A8;15: last updated on 02/Sep/19 Commented by mathmax by abdo last updated on 02/Sep/19 $${at}\:{form}\:{of}\:{serie} \\ $$$${I}\:=\int\sqrt{{e}^{{x}} }{dx}\:=\:\int\:\:{e}^{\frac{{x}}{\mathrm{2}}} {dx}\:=\int\left(\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(\frac{{x}}{\mathrm{2}}\right)^{{n}}…