Question Number 127726 by mnjuly1970 last updated on 01/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:{evaluate}:: \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\left(\frac{{ln}\left({cos}\left(\frac{{x}}{\mathrm{2}}\right)\right)−{ln}\left({cos}\left(\frac{{y}}{\mathrm{2}}\right)\right)}{{cos}\left({x}\right)−{cos}\left({y}\right)}\right){dxdy} \\ $$$$ \\ $$ Terms of Service…
Question Number 127725 by mnjuly1970 last updated on 01/Jan/21 $$\:\:\:\:\:\:\:…\:{advanced}\:\:{mathematics}… \\ $$$$\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{{n}} \begin{pmatrix}{\mathrm{3}{n}}\\{\:\:{n}}\end{pmatrix}}\:\overset{???} {=}\frac{\mathrm{3}}{\mathrm{125}}\left(\frac{\mathrm{11}\pi}{\mathrm{6}}−\mathrm{2}{log}\left(\mathrm{2}\right)+\mathrm{45}\right) \\ $$$$ \\ $$ Answered by Ar…
Question Number 127723 by bemath last updated on 01/Jan/21 $$\:\left(\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} \right)\:\mathrm{dx}\:−\mathrm{3xy}\:\mathrm{dy}\:=\:\mathrm{0}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62186 by aliesam last updated on 17/Jun/19 $$\int\frac{{e}^{\mathrm{3}{x}^{\mathrm{2}} } }{\:\sqrt[{\mathrm{8}}]{\mathrm{1}−{x}^{\mathrm{4}} }}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62185 by aliesam last updated on 17/Jun/19 $$\int\frac{{dx}}{{sin}\mathrm{3}{x}+{sin}\mathrm{4}{x}} \\ $$ Answered by MJS last updated on 17/Jun/19 $$\int\frac{{dx}}{\mathrm{sin}\:\mathrm{3}{x}\:+\mathrm{sin}\:\mathrm{4}{x}}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\mathrm{1}}{\mathrm{cos}\:{x}}\:\rightarrow\:{dx}=\frac{\mathrm{cos}^{\mathrm{2}} \:{x}}{\mathrm{sin}\:{x}}\right] \\ $$$$=−\int\frac{{t}^{\mathrm{3}}…
Question Number 62184 by aliesam last updated on 17/Jun/19 $$\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{1}}\:+\:\sqrt{\mathrm{3}{x}+\mathrm{1}}\:=\:\mathrm{3}\sqrt[{\mathrm{4}}]{{x}} \\ $$ Commented by MJS last updated on 17/Jun/19 $${x}=\mathrm{0}\:\vee\:{x}=\mathrm{1} \\ $$$$\mathrm{trying}\:\mathrm{2}{x}−\mathrm{1}={n}^{\mathrm{3}} \:\Rightarrow\:{x}=\frac{{n}^{\mathrm{3}} +\mathrm{1}}{\mathrm{2}} \\…
Question Number 127716 by liberty last updated on 01/Jan/21 $$\:\mathrm{Let}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{be}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number} \\ $$$$\mathrm{such}\:\mathrm{that}\:\begin{cases}{\mathrm{p}\sqrt{\mathrm{p}}\:+\mathrm{q}\sqrt{\mathrm{q}}\:=\:\mathrm{32}}\\{\mathrm{p}\sqrt{\mathrm{q}}\:+\:\mathrm{q}\sqrt{\mathrm{p}}\:=\:\mathrm{31}}\end{cases} \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{5}\left(\mathrm{p}+\mathrm{q}\right)?}{\mathrm{7}} \\ $$ Answered by mindispower last updated on 01/Jan/21 $$\left(\sqrt{{p}}+\sqrt{{q}}\right)^{\mathrm{3}} ={p}\sqrt{{p}}+{q}\sqrt{{q}}+\mathrm{3}\left({p}\sqrt{{q}}+{p}\sqrt{{q}}\right)=\mathrm{32}+\mathrm{3}.\mathrm{31}=\mathrm{125}…
Question Number 62180 by Mikael last updated on 17/Jun/19 $$\underset{{x}\rightarrow\infty} {{lim}}\:\frac{{senx}}{{x}} \\ $$ Commented by maxmathsup by imad last updated on 17/Jun/19 $${if}\:{you}\:{mean}\:{sinx}\:\:{we}\:{have}\:\:\mid{sinx}\mid\leqslant\mathrm{1}\:\Rightarrow\mid\frac{{sinx}}{{x}}\mid\leqslant\frac{\mathrm{1}}{\mid{x}\mid}\:\:{for}\:{all}\:{x}\neq\mathrm{0}\:\:{but} \\ $$$${lim}_{{x}\rightarrow\infty}…
Question Number 62179 by Tawa1 last updated on 16/Jun/19 $$\int_{\:\:\mathrm{0}} ^{\:\mathrm{2}\:\sqrt{\mathrm{ln}\:\mathrm{3}}} \:\int_{\:\:\frac{\mathrm{y}}{\mathrm{2}}} ^{\:\sqrt{\mathrm{ln}\:\mathrm{3}}} \:\:\:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\:\mathrm{dx}\:\mathrm{dy} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 127715 by snipers237 last updated on 01/Jan/21 $$\:\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\frac{\left({argshx}\right)^{\mathrm{2}} }{\mathrm{2}{cosx}}\:{dx}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com