Question Number 61614 by Tajaddin last updated on 05/Jun/19 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{{d}}{{dx}}\:\left(\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{x}}\right){dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 05/Jun/19 $${we}\:{have}\:\frac{{d}}{{dx}}\left({arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right)\:=\frac{−\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 60461 by ashutosh last updated on 21/May/19 $$\mathrm{Two}\:\mathrm{cogged}\:\mathrm{wheels},\:\mathrm{of}\:\mathrm{which}\:\mathrm{one}\:\mathrm{has} \\ $$$$\mathrm{16}\:\mathrm{cogs}\:\mathrm{and}\:\mathrm{other}\:\mathrm{has}\:\mathrm{27},\:\mathrm{work}\:\mathrm{into}\: \\ $$$$\mathrm{each}\:\mathrm{other}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{latter}\:\mathrm{turns}\:\mathrm{80}\:\mathrm{times}\:\mathrm{in}\: \\ $$$$\mathrm{three}\:\mathrm{quarters}\:\mathrm{of}\:\mathrm{a}\:\mathrm{minute},\:\mathrm{how}\:\mathrm{often} \\ $$$$\mathrm{does}\:\mathrm{the}\:\mathrm{other}\:\mathrm{turn}\:\mathrm{in}\:\mathrm{8}\:\mathrm{seconds}? \\ $$ Answered by MJS last updated…
Question Number 59976 by soufiane last updated on 16/May/19 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left(\frac{\pi}{\mathrm{2}}−{x}\right)}\:{dx}\:= \\ $$ Answered by tanmay last updated on 16/May/19 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left(\frac{\pi}{\mathrm{2}}−{x}\right)}{dx} \\…
Question Number 59714 by Khairun Nisa last updated on 13/May/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{four}\:\mathrm{digit}\:\mathrm{number} \\ $$$$\mathrm{which}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{18}\:\mathrm{and}\:\mathrm{12} \\ $$$$\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{of}\:\mathrm{4}\:\mathrm{in}\:\mathrm{each}\:\mathrm{case} \\ $$ Answered by tanmay last updated on 14/May/19 $$…
Question Number 59389 by hovea cw last updated on 09/May/19 $$\mathrm{If}\:\:\:\mathrm{0}\leqslant\:{x}\:\leqslant\:\pi\:\:\mathrm{and}\:\:\mathrm{81}^{\mathrm{sin}^{\mathrm{2}} {x}} +\:\mathrm{81}^{\mathrm{cos}^{\mathrm{2}} {x}} =\mathrm{30}, \\ $$$$\mathrm{then}\:\:{x}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by ajfour last updated on…
Question Number 59177 by 2772639291927 last updated on 05/May/19 $$\int\:\:\frac{\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{cos}\:{x}}\:{dx}\:= \\ $$ Commented by mathsolverby Abdo last updated on 05/May/19 $${I}\:=\int\frac{\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}}{{cosx}}{dx}\:=\int\mathrm{2}{cosx}\:{dx}−\int\frac{{dx}}{{cosx}} \\ $$$${but}\:\int\:\mathrm{2}{cosxdx}\:=\mathrm{2}{sinx}\:+{c}_{\mathrm{1}} \\…
Question Number 59170 by 2772639291927 last updated on 05/May/19 $$\mathrm{If}{f}\left({x}\right)=\begin{vmatrix}{\mathrm{sec}\:{x}}&{\mathrm{cos}\:{x}}&{\mathrm{sec}^{\mathrm{2}} {x}+\mathrm{cosec}\:{x}\:\mathrm{cot}\:{x}}\\{\mathrm{cos}^{\mathrm{2}} {x}}&{\mathrm{cos}^{\mathrm{2}} {x}}&{\:\:\:\:\:\:\:\:\:\:\mathrm{cosec}^{\mathrm{2}} {x}}\\{\:\:\:\mathrm{1}}&{\mathrm{cos}^{\mathrm{2}} {x}}&{\:\:\:\:\:\:\:\:\:\:\mathrm{cos}^{\mathrm{2}} {x}}\end{vmatrix} \\ $$$$\mathrm{then}\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:{f}\left({x}\right)\:{dx}\:= \\ $$ Answered by MJS…
Question Number 59049 by ugwu Kingsley last updated on 03/May/19 $$\:\underset{\:\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{x}\:\mathrm{log}\:{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 58211 by salaw2000 last updated on 20/Apr/19 $$\underset{\:\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\:\mid\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:\mid{dx}\:= \\ $$ Commented by tanmay last updated on 20/Apr/19 Commented by tanmay last…
Question Number 58177 by mamah Fousséni last updated on 19/Apr/19 $$\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{2}\:\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\:\:= \\ $$ Answered by math1967 last updated on 19/Apr/19 $$\frac{\pi}{\mathrm{3}}+\mathrm{2}×\frac{\pi}{\mathrm{6}}=\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$…