Question Number 57992 by Tinkutara last updated on 15/Apr/19 Answered by MJS last updated on 16/Apr/19 $$\underset{\mathrm{1}} {\overset{{c}} {\int}}\left(−{x}^{\mathrm{5}} +\mathrm{8}{x}^{\mathrm{2}} \right){dx}=\frac{\mathrm{16}}{\mathrm{3}} \\ $$$$−\frac{\mathrm{1}}{\mathrm{6}}{c}^{\mathrm{6}} +\frac{\mathrm{8}}{\mathrm{3}}{c}^{\mathrm{3}} −\frac{\mathrm{5}}{\mathrm{2}}=\frac{\mathrm{16}}{\mathrm{3}}…
Question Number 57991 by Tinkutara last updated on 15/Apr/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 189057 by neinhaltsieger369 last updated on 11/Mar/23 $$\: \\ $$$$\:\mathrm{Help}! \\ $$$$\: \\ $$$$\:\mathrm{Evaluate}\:\:\mathrm{the}\:\:\mathrm{following}\:\:\mathrm{integral}\:\:\mathrm{usings}\:\:\mathrm{Green}\:\mathrm{theorem}: \\ $$$$\: \\ $$$$\:\oint\mathrm{4xy}{d}\mathrm{x}\:\:+\:\:\mathrm{x}^{\mathrm{2}} {d}\mathrm{y} \\ $$$$\: \\ $$$$\:\mathrm{Where}\:\:{C}\:\:\mathrm{is}\:\:\mathrm{the}\:\:\mathrm{square}\:\:\mathrm{of}\:\:\mathrm{vertices}\:\:\left(\mathrm{0},\mathrm{0}\right),\:\left(\mathrm{0},\mathrm{2}\right),\:\left(\mathrm{2},\mathrm{0}\right)\:\:\mathrm{and}\:\:\left(\mathrm{2},\mathrm{2}\right).…
Question Number 123513 by bramlexs22 last updated on 26/Nov/20 $$\int\:\frac{\mathrm{sin}\:{x}+\mathrm{2cos}\:{x}}{\mathrm{3sin}\:{x}+\mathrm{4cos}\:{x}}\:{dx}? \\ $$ Commented by liberty last updated on 26/Nov/20 $${by}\:{partial}\:{fraction} \\ $$$${o}\left({x}\right)=\frac{\mathrm{11}}{\mathrm{25}}\int\:\frac{\mathrm{3sin}\:{x}+\mathrm{4cos}\:{x}}{\mathrm{3sin}\:{x}+\mathrm{4cos}\:{x}}{dx}+\frac{\mathrm{2}}{\mathrm{25}}\int\:\frac{\mathrm{3cos}\:{x}−\mathrm{4sin}\:{x}}{\mathrm{3sin}\:{x}+\mathrm{4cos}\:{x}}{dx} \\ $$$${o}\left({x}\right)=\frac{\mathrm{11}{x}}{\mathrm{25}}+\frac{\mathrm{2}}{\mathrm{25}}\ell{n}\:\mid\mathrm{3sin}\:{x}+\mathrm{4cos}\:{x}\mid\:+\:{c}\: \\…
Question Number 123494 by bemath last updated on 25/Nov/20 $$\:\int\:\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right)\:\sqrt{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}}}\:{dx}\:? \\ $$ Answered by bramlexs22 last updated on 26/Nov/20 $$\:{I}\left({x}\right)=\int\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} +{x}^{\mathrm{2}}…
Question Number 123495 by bemath last updated on 25/Nov/20 $$\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{x}−\mathrm{1}}{\left(\mathrm{2}−\sqrt{{x}}\right)\left(\mathrm{1}−{x}^{\mathrm{3}} \right)}\:{dx}\:? \\ $$ Answered by MJS_new last updated on 26/Nov/20 $$\int\frac{{x}−\mathrm{1}}{\left(\mathrm{2}+\sqrt{{x}}\right)\left(\mathrm{1}−{x}^{\mathrm{3}} \right)}{dx}=\int\frac{{dx}}{\left(\sqrt{{x}}−\mathrm{2}\right)\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)}=…
Question Number 57948 by maxmathsup by imad last updated on 14/Apr/19 $${let}\:{A}\left(\xi\right)\:=\int_{\xi} ^{\xi^{\mathrm{2}} } \:\:\:\:\frac{{arctan}\left(\mathrm{1}+\xi{t}\right)−\frac{\pi}{\mathrm{4}}}{\:\sqrt{\mathrm{2}+\xi{t}}−\sqrt{\mathrm{2}−\xi{t}}}\:{dt} \\ $$$${find}\:{lim}_{\xi\:\rightarrow\mathrm{0}} \:\:{A}\left(\xi\right)\:. \\ $$$$ \\ $$ Terms of Service…
Question Number 123462 by mnjuly1970 last updated on 25/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}}\:\overset{??} {=}\frac{\mathrm{11}\zeta\left(\:\mathrm{3}\:\right)}{\mathrm{8}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…………….. \\ $$ Answered by Lordose…
Question Number 123456 by mnjuly1970 last updated on 25/Nov/20 $$\:\:\:\:\:\:…\:{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}:: \\ $$$$\:\:\:\:\:\:\:\:\:\phi=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\:\frac{\mathrm{H}_{{n}} }{{n}^{\mathrm{3}} }\:\right)\overset{???} {=}\frac{\pi^{\mathrm{4}} }{\mathrm{72}} \\ $$$$\:\:\:\:\:\:\:{note}:\:\mathrm{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+…+\frac{\mathrm{1}}{{n}} \\ $$…
Question Number 123452 by Eric002 last updated on 25/Nov/20 $$\int\frac{{dx}}{\:\left({x}^{\mathrm{2}} +{n}\right)\sqrt{{x}^{\mathrm{2}} +{a}}} \\ $$ Commented by MJS_new last updated on 25/Nov/20 $$\mathrm{depends}\:\mathrm{on}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{a}\:\mathrm{and}\:{n}\:\mathrm{and}\:\mathrm{their} \\ $$$$\mathrm{relation}… \\…