Question Number 545 by 123456 last updated on 25/Jan/15 $${if}\:\tau=\underset{\mathrm{0}} {\overset{+\infty} {\int}}{e}^{−\frac{{t}}{\mathrm{2}}} {dt}\underset{−\infty} {\overset{+\infty} {\int}}\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} },\:{then}\:\frac{\tau}{\mathrm{2}}=? \\ $$ Answered by prakash jain last updated on…
Question Number 131618 by physicstutes last updated on 06/Feb/21 $$\:\left(\mathrm{1}\right)\:\mathrm{A}\:\mathrm{cell}\:\mathrm{has}\:\mathrm{an}\:\mathrm{Emf}\:\mathrm{of}\:\mathrm{2}.\mathrm{5}\:\mathrm{V}\:.\mathrm{It}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{balanced}\:\mathrm{by}\:\mathrm{a}\: \\ $$$$\mathrm{potentiometer}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{100}.\mathrm{0}\:\mathrm{cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{driver}\:\mathrm{cell}\:\mathrm{of}\:\mathrm{of}\:\mathrm{2}.\mathrm{0V} \\ $$$$\mathrm{is}\:\mathrm{connected}\:\mathrm{to}\:\mathrm{it}.\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{best}\:\mathrm{explains}\:\mathrm{why}\:\mathrm{there} \\ $$$$\mathrm{is}\:\mathrm{no}\:\mathrm{balance}\:\mathrm{lenght}? \\ $$$$\:\mathrm{A}.\:\mathrm{The}\:\mathrm{current}\:\mathrm{in}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{is}\:\mathrm{too}\:\mathrm{low}.\:\:\:\:\:\:\:\mathrm{B}.\:\mathrm{the}\:\mathrm{balance}\:\mathrm{lenght}\:\mathrm{is}\:\mathrm{too}\:\mathrm{small} \\ $$$$\:\mathrm{C}.\:\mathrm{the}\:\mathrm{emf}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cell}\:\mathrm{is}\:\mathrm{too}\:\mathrm{low}.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{The}\:\mathrm{voltae}\:\mathrm{accross}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{is}\:\mathrm{too}\:\mathrm{low}. \\ $$$$\mathrm{please}\:\mathrm{site}\:\mathrm{a}\:\mathrm{little}\:\mathrm{explanation}. \\ $$ Terms…
Question Number 544 by 123456 last updated on 26/Jan/15 $$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\mathrm{sin}\:{x}\:\mathrm{sinh}\:{x}\:{dx}=? \\ $$ Answered by prakash jain last updated on 26/Jan/15 $$\int\mathrm{sin}\:{x}\:\mathrm{sinh}\:{xdx} \\ $$$$=\mathrm{sin}\:{x}\:\mathrm{cosh}\:{x}\:−\int\mathrm{cos}\:{x}\:\mathrm{cosh}\:{x}\:{dx}…
Question Number 131613 by mohammad17 last updated on 06/Feb/21 $$\frac{{z}^{\mathrm{3}} +\mathrm{8}}{{z}^{\mathrm{4}} +\mathrm{4}{z}^{\mathrm{2}} +\mathrm{16}} \\ $$ Answered by Dwaipayan Shikari last updated on 06/Feb/21 $$\frac{{z}^{\mathrm{3}} +\mathrm{8}}{{z}^{\mathrm{4}}…
Question Number 543 by 123456 last updated on 25/Jan/15 $${if}\:{f}'\left({x}\right)={f}\left({x}\right)+{x},\:{f}\left(\mathrm{0}\right)=\mathrm{0},\:{then} \\ $$$${f}\left(\mathrm{1}\right)=? \\ $$ Answered by prakash jain last updated on 24/Jan/15 $${y}={f}\left({x}\right) \\ $$$${y}'−{y}={x}…
Question Number 542 by 123456 last updated on 25/Jan/15 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{6}} +\mathrm{4}}}{dx} \\ $$ Answered by prakash jain last updated on 24/Jan/15 $${x}^{\mathrm{3}}…
Question Number 131614 by mnjuly1970 last updated on 06/Feb/21 $$\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:{prove}\:{that}\::\: \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right){cos}\left(\mathrm{2}\pi{nx}\right){dx}=\frac{\mathrm{1}}{\mathrm{4}{n}} \\ $$$${for}\:{example}\::\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right){cos}\left(\mathrm{2}\pi{x}\right){dx}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Terms of Service…
Question Number 537 by kth last updated on 25/Jan/15 $$\int_{\mathrm{4}} ^{\mathrm{5}} \frac{{x}−\mathrm{2}}{\left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}\right)^{\mathrm{3}} }{dx} \\ $$ Answered by Vishal last updated on 25/Jan/15 $${let}\:{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}\:=\:{t}\:{then}\:\left({x}−\mathrm{2}\right)\:{dx}\:=\:\frac{{dt}}{\mathrm{2}}…
Question Number 536 by kth last updated on 25/Jan/15 $$\int_{\mathrm{1}} ^{\mathrm{4}} \frac{\mathrm{2}}{\:\sqrt{{x}}\left(\sqrt{{x}}+\mathrm{4}\right)^{\mathrm{3}} }{dx} \\ $$$$ \\ $$ Answered by Vishal last updated on 24/Jan/15 $${let}\:\sqrt{{x}}+\mathrm{4}={t}\:{then}\:\frac{\mathrm{1}}{\:\sqrt{{x}}}\:{dx}=\mathrm{2}\:{dt}…
Question Number 131605 by physicstutes last updated on 06/Feb/21 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:{m}^{\mathrm{4}} −\mathrm{7}{m}^{\mathrm{3}} +\:\mathrm{14}{m}^{\mathrm{2}} −\mathrm{7}{m}\:+\:\mathrm{1}\:=\:\mathrm{0}\: \\ $$ Answered by malwan last updated on 06/Feb/21 $${m}^{\mathrm{4}}…