Question Number 209332 by efronzo1 last updated on 07/Jul/24 Answered by Frix last updated on 07/Jul/24 $${x}^{\mathrm{3}} −\mathrm{8}{x}^{\mathrm{2}} +\left(\mathrm{16}−{k}\right){x}=\mathrm{0} \\ $$$${x}_{\mathrm{1}} =\mathrm{0}\:\:{x}_{\mathrm{2}} =\mathrm{4}−\sqrt{{k}}\:\:{x}_{\mathrm{3}} =\mathrm{4}+\sqrt{{k}} \\…
Question Number 209217 by mnjuly1970 last updated on 04/Jul/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{calculate}}\:: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\:\int_{\mathrm{0}\:} ^{\:\infty} \frac{\:{tan}^{\:−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}\:+\:{x}^{\:\mathrm{2}} \right)^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\: \\ $$$$ \\ $$…
Question Number 208900 by KradecaNaLukcheta last updated on 26/Jun/24 $${Does}\:{anyone}\:{know}\:{of}\:{an}\:{intuition} \\ $$$${behind}\:{the}\:{integral}\:{form}\:{of}\:{the} \\ $$$${remainder}\:{in}\:{Taylor}'{s}\:{theorem}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 208871 by Shrodinger last updated on 26/Jun/24 $${L}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{4}−\mathrm{3}{x}}{\mathrm{4}+\mathrm{5}{x}}}{dx} \\ $$ Answered by Sutrisno last updated on 26/Jun/24 $${misal} \\ $$$$\sqrt{\frac{\mathrm{4}−\mathrm{3}{x}}{\mathrm{4}+\mathrm{5}{x}}}={p}\rightarrow{x}=\frac{−\mathrm{4}{p}^{\mathrm{2}} +\mathrm{4}}{\mathrm{5}{p}^{\mathrm{2}}…
Question Number 208842 by NasaSara last updated on 24/Jun/24 $${does}\:{the}\:{rule}\:{of}\:{odd}\:{and}\:{even}\:{functions}\: \\ $$$${can}\:{be}\:{applied}\:{with}\:{improper}\:{integration}? \\ $$$${I}=\int_{−\infty} ^{\infty} {xe}^{−{x}^{\mathrm{2}} } {dx}\: \\ $$$${while}\:\:{f}\left({x}\right)=\:{xe}^{−{x}^{\mathrm{2}} } \:{is}\:{odd} \\ $$$${then}\:{I}\:=\mathrm{0} \\…
Question Number 208791 by MATHEMATICSAM last updated on 23/Jun/24 $$\mathrm{If}\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \left(\mathrm{1}\:+\:{x}^{\mathrm{6}} \right)^{\frac{\mathrm{2}}{\mathrm{3}}} }\:=\:{xf}\left({x}\right).\left(\mathrm{1}\:+\:{x}^{\mathrm{6}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:{C}\: \\ $$$$\mathrm{where}\:{C}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{integration}\:\mathrm{then} \\ $$$$\mathrm{find}\:{f}\left({x}\right). \\ $$ Commented by mr W…
Question Number 208805 by Mastermind last updated on 23/Jun/24 $$\mathrm{Integrate}: \\ $$$$\left(\mathrm{xdz}\:−\:\mathrm{zdx}\right)\:−\:\mathrm{a}^{\mathrm{2}} \left(\mathrm{2xzdz}\:−\:\mathrm{z}^{\mathrm{2}} \mathrm{dx}\right)\:+\:\mathrm{2x}^{\mathrm{3}} \:=\:\mathrm{0} \\ $$ Commented by mr W last updated on 23/Jun/24…
Question Number 208692 by Ghisom last updated on 21/Jun/24 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}\mathrm{ln}\:\mathrm{sin}\:{x}\:{dx}=? \\ $$ Answered by Berbere last updated on 21/Jun/24 $${ln}\left({sin}\left({x}\right)\right)=−{ln}\left(\mathrm{2}\right)−\underset{{k}\geqslant\mathrm{1}} {\sum}\frac{{cos}\left(\mathrm{2}{kx}\right)}{{k}} \\ $$$${proof}\:{ln}\left({sin}\left({x}\right)\right)={Re}\left({ln}\left({sin}\left({x}\right)\right)\right.…
Question Number 208693 by Frix last updated on 21/Jun/24 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{area}\:\mathrm{enclosed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\left(\frac{\mathrm{1}}{{x}}−\mathrm{2}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{{y}}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{1} \\ $$ Answered by mr W last updated on 21/Jun/24 $$\frac{\mathrm{1}}{{x}}−\mathrm{2}={u}\:\Rightarrow{x}=\frac{\mathrm{1}}{\mathrm{2}+{u}}…
Question Number 208733 by Frix last updated on 22/Jun/24 $$\mathrm{2}\underset{\frac{\mathrm{1}}{\mathrm{3}}} {\overset{\mathrm{1}} {\int}}\frac{{x}\sqrt{−\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{1}}}{\mathrm{7}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}{dx}=? \\ $$$$\mathrm{Exact}\:\mathrm{solution}\:\mathrm{needed}. \\ $$ Answered by Ghisom last updated on 24/Jun/24…