Question Number 137837 by Ñï= last updated on 07/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:{x}−\mathrm{sin}\:{x}^{\mathrm{2}} }{{x}}=\frac{\pi}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{cos}\:{x}−\mathrm{cos}\:{x}^{\mathrm{2}} }{{x}}{dx}=−\frac{\gamma}{\mathrm{2}} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 72296 by naka3546 last updated on 27/Oct/19 $${Let}\:\:\:\:{x}\:\:=\:\:{f}\left({x}\right)\:{e}^{{f}\left({x}\right)} \\ $$$$\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}\overset{\:{e}} {\:}{f}\left({x}\right)\:{dx}\:\:=\:\:? \\ $$ Commented by naka3546 last updated on 27/Oct/19 $${e}^{\mathrm{ln}\:{x}} \:\:=\:\:{x}…
Question Number 6762 by 314159 last updated on 24/Jul/16 Commented by Yozzii last updated on 24/Jul/16 $${x}_{\mathrm{1}} ^{\mathrm{2}} +{x}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{1}} {x}_{\mathrm{2}} {cos}\theta=\mathrm{1}, \\ $$$${y}_{\mathrm{1}}…
Question Number 72275 by Maclaurin Stickker last updated on 27/Oct/19 $$\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{X}_{{i}} =\mathrm{42} \\ $$$${Find}\:{X}_{\mathrm{1}} \:{and}\:{X}_{\mathrm{3}} \\ $$ Commented by mind is power last…
Question Number 137784 by mathocean1 last updated on 06/Apr/21 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{6}}} \frac{{dx}}{{sinx}}=? \\ $$$$ \\ $$ Answered by EnterUsername last updated on 06/Apr/21 $$\int\frac{{dx}}{{sinx}}={ln}\mid{cosecx}−{cotx}\mid+{C} \\…
Question Number 137787 by physicstutes last updated on 06/Apr/21 $$\mathrm{A}\:\mathrm{string}\:{AB}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{2}{l}\:\mathrm{has}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{its}\:\mathrm{midpoint}\:\mathrm{C}.\: \\ $$$$\mathrm{The}\:\mathrm{ends}\:{A}\:\mathrm{and}\:{B}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string}\:\mathrm{are}\:\mathrm{fastened}\:\mathrm{to}\:\mathrm{two}\:\mathrm{fixed}\:\mathrm{points} \\ $$$$\mathrm{with}\:{A}\:\mathrm{distance}\:{l}\:\mathrm{vertically}\:\mathrm{above}\:\mathrm{B}.\mathrm{With}\:\mathrm{both}\:\mathrm{parts}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string} \\ $$$$\mathrm{taunt},\mathrm{the}\:\mathrm{particle}\:\mathrm{describes}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{circle}\:\mathrm{about}\:\mathrm{the}\:\mathrm{line}\:{AB}\:\mathrm{with} \\ $$$$\mathrm{constant}\:\mathrm{angular}\:\mathrm{speed}\:\omega.\:\mathrm{If}\:\mathrm{the}\:\mathrm{tension}\:\mathrm{in}\:{CA}\:\mathrm{is}\:\mathrm{three}\:\mathrm{times} \\ $$$$\mathrm{that}\:\mathrm{in}\:{CB},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{angular}\:\mathrm{velocity}\:\mathrm{is}\:\mathrm{2}\sqrt{\frac{\mathrm{g}}{{l}}}\:. \\ $$ Answered by mr…
Question Number 137783 by otchereabdullai@gmail.com last updated on 06/Apr/21 $$\mathrm{Some}\:\mathrm{birds}\:\mathrm{were}\:\mathrm{flying}\:\mathrm{and}\:\mathrm{met}\:\mathrm{a}\: \\ $$$$\mathrm{bird},\:\mathrm{the}\:\mathrm{bird}\:\mathrm{greeted}\:\mathrm{them}\:\mathrm{and}\:\mathrm{said} \\ $$$$\mathrm{how}\:\mathrm{are}\:\mathrm{you}\:\mathrm{hundred}.\:\mathrm{The}\:\mathrm{birds}\:\mathrm{said} \\ $$$$\mathrm{we}\:\mathrm{are}\:\mathrm{not}\:\mathrm{hundred},\:\mathrm{we}\:\mathrm{need}\:\mathrm{half}\:\mathrm{of}\:\mathrm{us} \\ $$$$\mathrm{plus}\:\mathrm{you}\:\mathrm{to}\:\mathrm{make}\:\mathrm{hundred}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{birds}\:\mathrm{were}\:\mathrm{flying} \\ $$ Answered by physicstutes…
Question Number 137721 by Ñï= last updated on 05/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{2}} }=? \\ $$$${except}\:{use}\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{2}} }=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}−\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}},{any}\:{other}\:{way}? \\ $$ Answered by TANMAY…
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Question Number 6644 by WAI LIN last updated on 07/Jul/16 $${Prove}\:\frac{{d}}{{dt}}\:{e}_{\rho} =\phi\:{e}_{\phi} \:,\:\frac{{d}}{{dt}}\:{e}_{\phi} =\:−\phi\:{e}_{\rho} \:{where}\:{dots}\:{denote}\: \\ $$$${differentiation}\:{with}\:{respect}\:{to}\:{time}\:{t}. \\ $$ Terms of Service Privacy Policy Contact:…