Question Number 1985 by 123456 last updated on 27/Oct/15 $${f}:\left[{a},{b}\right]\rightarrow\mathbb{R} \\ $$$$\underset{{a}} {\overset{{b}} {\int}}{fdx}=\underset{{a}} {\overset{{b}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dx}}\right)^{\mathrm{2}} }{dx} \\ $$$$\mathrm{does} \\ $$$$\pi\underset{{a}} {\overset{{b}} {\int}}{f}^{\mathrm{2}} {dx}=\mathrm{2}\pi\underset{{a}} {\overset{{b}}…
Question Number 1970 by 123456 last updated on 27/Oct/15 $${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$${xf}\left({x}\right)={f}\left[{f}\left({x}\right)\right]{f}\left({x}\right) \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 27/Oct/15 $${f}\left({x}\right)\neq\mathrm{0}\:\mathrm{then}\:{f}\left({f}\left({x}\right)={x}\right.…
Question Number 1964 by 123456 last updated on 26/Oct/15 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{{cy}}{{x}^{\mathrm{2}} } \\ $$$${y}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 26/Oct/15…
Question Number 67482 by Rasheed.Sindhi last updated on 27/Aug/19 $${I}\:{have}\:{tried}\:{to}\:{solve}\:{Q}#\mathrm{67299} \\ $$$${Please}\:{see}\:{and}\:{give}\:{critical}\:{remarks} \\ $$ Commented by mr W last updated on 28/Aug/19 $${your}\:{solution}\:{is}\:{correct}\:{sir}.\:{but}\:{i}'{m} \\ $$$${not}\:{sure}\:{if}\:{the}\:{solution}\:{is}\:{unique}.…
Question Number 1936 by 123456 last updated on 25/Oct/15 $${f}^{\mathrm{2}} \left({x}\right)−{f}\left({x}^{\mathrm{2}} \right)={a}\:\left[\mathrm{G}.\mathrm{Q1902}\right] \\ $$$${f}\left({x}\right)=? \\ $$ Commented by prakash jain last updated on 25/Oct/15 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{that}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{exists}\:\mathrm{except}…
Question Number 67471 by AnjanDey last updated on 27/Aug/19 $$\boldsymbol{{Evaluate}}:\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}}\:{dx} \\ $$ Commented by MJS last updated on 28/Aug/19 $$\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}{dt}\right] \\ $$$$=\mathrm{2}\int{t}^{\mathrm{2}} \left({t}^{\mathrm{2}}…
Question Number 1862 by 123456 last updated on 17/Oct/15 $${f}\left[{x}−{f}\left({y}\right)\right]={f}\left({x}\right)−{f}\left({y}\right),\forall\left({x},{y}\right)\in\mathbb{R} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 18/Oct/15 $${f}\left({x}\right)={x}\:\mathrm{is}\:\mathrm{one}\:\mathrm{solution}.…
Question Number 1861 by 123456 last updated on 17/Oct/15 $$\mathrm{V}\left(\xi\right)=\pi\rho^{\mathrm{2}} \underset{−\infty} {\overset{\xi} {\int}}{e}^{\mathrm{2}{z}} {dz} \\ $$$$\mathrm{S}\left(\xi\right)=\mathrm{2}\pi\rho\underset{−\infty} {\overset{\xi} {\int}}{e}^{{z}} \sqrt{\mathrm{1}+\rho^{\mathrm{2}} {e}^{\mathrm{2}{z}} }{dz} \\ $$$$\mathrm{V}\left(\xi\right)−\mathrm{S}\left(\xi\right)=? \\ $$…
Question Number 1850 by 123456 last updated on 14/Oct/15 $${f}_{{n}+\mathrm{1}} \left({z}+\mathrm{1}\right)=\left[{z}−{f}_{{n}} \left(\mathrm{0}\right)\right]{f}_{{n}} \left({z}\right) \\ $$$${f}_{\mathrm{1}} \left({z}\right)={z}+\mathrm{1} \\ $$$${f}_{\mathrm{3}} \left({z}\right)=??? \\ $$ Answered by Rasheed Soomro…
Question Number 1848 by 123456 last updated on 14/Oct/15 $${f}_{{n}+\mathrm{1}} \left({z}+\mathrm{1}\right)=\left[{z}−{f}_{{n}−\mathrm{1}} \left(\mathrm{0}\right)\right]{f}_{{n}} \left({z}\right) \\ $$$${f}_{\mathrm{0}} \left({z}\right)=\mathrm{0} \\ $$$${f}_{\mathrm{1}} \left({z}\right)={z}+\mathrm{1} \\ $$$${f}_{\mathrm{3}} \left({z}\right)=???? \\ $$ Answered…