Question Number 125421 by bemath last updated on 11/Dec/20 $$\:\underset{\mathrm{0}} {\overset{\mathrm{100}} {\int}}\:\frac{{dx}}{\:\sqrt{{x}\left(\mathrm{100}−{x}\right)}}\:?\: \\ $$ Answered by liberty last updated on 11/Dec/20 $${I}=\underset{\mathrm{0}} {\overset{\mathrm{100}} {\int}}\:\frac{{dx}}{\:\sqrt{{x}}\:\sqrt{\mathrm{100}−{x}}}\:;\:{let}\:\sqrt{{x}}\:=\:\mathrm{10}\:\mathrm{sin}\:{t}\: \\…
Question Number 125416 by bemath last updated on 10/Dec/20 $$\int\:\frac{{dx}}{\:\sqrt{{x}\sqrt{{x}}−{x}^{\mathrm{2}} }}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 10/Dec/20 $$\int\frac{{dx}}{\:\sqrt{{x}}\sqrt{\sqrt{{x}}−{x}}}\:\:\:\:\:\:\:\:\:\:\sqrt{{x}}={t}\Rightarrow\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}=\frac{{dt}}{{dx}} \\ $$$$=\mathrm{2}\int\frac{{dt}}{\:\sqrt{{t}−{t}^{\mathrm{2}} }}=\mathrm{2}\int\frac{\mathrm{1}}{\:\sqrt{{t}}\left(\sqrt{\mathrm{1}−{t}}\right)}{dt}\:\:\:\:\:\:\:\:\:\:\:\:\:{t}={u}^{\mathrm{2}}…
Question Number 59882 by aliesam last updated on 15/May/19 $$\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left({x}\right)}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 15/May/19 $${you}\:{are}\:{welcome}.…
Question Number 190940 by Spillover last updated on 14/Apr/23 $$\mathrm{The}\:\mathrm{parametric}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{curve}\:\:\mathrm{are} \\ $$$$\mathrm{x}=\mathrm{3t}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}=\mathrm{3t}−\mathrm{t}^{\mathrm{2}} . \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{generated} \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curve} \\ $$$$,\mathrm{the}\:\mathrm{x}−\mathrm{axis}\:\mathrm{and}\:\mathrm{the}\:\mathrm{ordinates}\: \\ $$$$\mathrm{corresponding}\:\mathrm{to}\: \\ $$$$\mathrm{t}=\mathrm{0}\:\:\:\mathrm{and}\:\mathrm{t}=\mathrm{2}\:\:\mathrm{rotates}\:\mathrm{about}\:\mathrm{the}\:\mathrm{y}−\mathrm{axis} \\…
Question Number 190937 by Spillover last updated on 14/Apr/23 $$\mathrm{Show}\:\:\mathrm{that}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{sech}\:\sqrt{\mathrm{x}}\:\mathrm{tanh}\:\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{x}}}=−\frac{\mathrm{2}}{\mathrm{cosh}\:\sqrt{\mathrm{x}}} \\ $$ Answered by ARUNG_Brandon_MBU last updated on 15/Apr/23 $${I}=\int\frac{\left(\mathrm{sech}\sqrt{{x}}\right)\left(\mathrm{tanh}\sqrt{{x}}\right)}{\:\sqrt{{x}}}{dx}=\int\frac{\mathrm{sinh}\sqrt{{x}}}{\:\sqrt{{x}}\mathrm{cosh}^{\mathrm{2}} \sqrt{{x}}}{dx} \\ $$$${t}=\mathrm{cosh}\sqrt{{x}}\:\Rightarrow{dt}=\frac{\mathrm{sinh}\sqrt{{x}}}{\mathrm{2}\sqrt{{x}}}{dx}…
Question Number 125390 by mnjuly1970 last updated on 10/Dec/20 $$\:\:\:\:\:\:\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{evaluate}\:::::\curvearrowright \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\sqrt{{x}}\:{tan}^{−\mathrm{1}} \left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=??? \\ $$ Answered by mathmax by abdo…
Question Number 125381 by liberty last updated on 10/Dec/20 $$\:{F}\left({x}\right)\:=\:\mathrm{cos}\:\left(\underset{\mathrm{1}} {\overset{{x}} {\int}}\:\mathrm{cos}\:\left(\underset{\mathrm{1}} {\overset{{t}} {\int}}\:\mathrm{sin}\:^{\mathrm{3}} {u}\:{du}\:\right){dy}\right) \\ $$$$\:\frac{{dF}\left({x}\right)}{{dx}}\:=\:?\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 59846 by bhanukumarb2@gmail.com last updated on 15/May/19 Commented by MJS last updated on 15/May/19 $$\mathrm{do}\:\mathrm{you}\:\mathrm{have}\:\mathrm{an}\:\mathrm{answer}? \\ $$$$\mathrm{it}\:\mathrm{seems}\:\mathrm{to}\:\mathrm{be}\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Commented by bhanukumarb2@gmail.com last…
Question Number 59834 by bhanukumarb2@gmail.com last updated on 15/May/19 Answered by tanmay last updated on 15/May/19 $$\mathrm{1}>{sin}\left(\mathrm{3}{x}\right)>−\mathrm{1} \\ $$$$\:\left({x}−\mathrm{1}\right)\geqslant{x}+{sin}\left(\mathrm{3}{x}\right)\geqslant{x}−\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\pi} {sin}^{\mathrm{4}} \left({x}+\mathrm{1}\right){dx}\geqslant\int_{\mathrm{0}} ^{\pi}…
Question Number 59825 by aliesam last updated on 15/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com