Question Number 130315 by stelor last updated on 24/Jan/21 Answered by Dwaipayan Shikari last updated on 24/Jan/21 $$\int_{−\infty} ^{\infty} {xe}^{−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}} {dx}\:\:\:\:\:\:\:\:\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}={u}\Rightarrow{x}=\frac{{du}}{{dx}} \\ $$$$=\int_{−\infty}…
Question Number 64778 by aliesam last updated on 21/Jul/19 Commented by som(math1967) last updated on 21/Jul/19 $${join}\:{O},{Q}\:\:{O},{N}\:{O},{M}\:\:{M},{Q}\:{N},{Q} \\ $$$${now}\:{ON}={NQ}={OQ}={OM}={MQ} \\ $$$$\therefore\angle{NOM}=\mathrm{60}+\mathrm{60}=\mathrm{120}° \\ $$$$\angle{MLN}=\frac{\mathrm{1}}{\mathrm{2}}\angle{NOM}=\mathrm{60}° \\ $$$$\angle{NKM}=\angle{NOM}=\mathrm{120}°\:\:\left[{subtend}\:{on}\:{same}\:{segment}\right]…
Question Number 64775 by Rio Michael last updated on 21/Jul/19 Commented by Rio Michael last updated on 21/Jul/19 $${the}\:{figure}\:{above}\:{shows}\:{a}\:{string}\:{PQRS}\:,\:{P}\:{and}\:{S}\:{are}\:{attached}\:{to}\:{a}\:{fixed}\:{support}\:{and} \\ $$$${mass}\:,{m},\:{and}\:\mathrm{2}.\mathrm{5}\:\mathrm{kg}\:{are}\:{attached}\:{at}\:{the}\:{points}\:{Q}\:{and}\:{R}\:{respectively}\:{and}\:{the}\:{system} \\ $$$${is}\:{in}\:{equilibruim}.\:{Calculate} \\ $$$$\left.{a}\right)\:{the}\:{mass},{m}.…
Question Number 64773 by ankan0 last updated on 21/Jul/19 $$\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}/\sqrt{\left.\mathrm{5}\right)}+\mathrm{cot}^{−\mathrm{1}} \mathrm{3}\right. \\ $$ Answered by Kunal12588 last updated on 21/Jul/19 $$\mathrm{cot}^{−\mathrm{1}} \left({a}\right)=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{a}^{\mathrm{2}} }}\right)…
Question Number 130306 by benjo_mathlover last updated on 24/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{x}\:\mathrm{cos}\:\left(\mathrm{x}\right)\:\mathrm{ln}\:\left(\mathrm{x}\right)\mathrm{e}^{−\mathrm{x}} \:\mathrm{dx}\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 24/Jan/21 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 130307 by mnjuly1970 last updated on 24/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:….\:\:\:\:\:{cslculus}… \\ $$$$\:\:\:{evaluate}\::::\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\:\left({x}\:\right)}{\:\sqrt{{x}}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:{dx}=? \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 130303 by stelor last updated on 24/Jan/21 $$\mathrm{hello}…\:\mathrm{please}\:\mathrm{give}\:\mathrm{me}\:\mathrm{the}\:\mathrm{limited}\:\mathrm{development}\:\mathrm{of}…{f}…\:{in}\:\mathrm{0}\:{at}\:\mathrm{3}^{{rd}} \:{order}. \\ $$$$\:\:\:\:{f}\left({x}\right)={ln}\left({sin}\left({x}\right)\right) \\ $$$$ \\ $$ Commented by stelor last updated on 24/Jan/21 $$\mathrm{developpement}\:\mathrm{limite}\:\mathrm{en}\:\frac{\Pi}{\mathrm{2}}\:\mathrm{a}\:\mathrm{l}'\mathrm{ordre}\:\mathrm{3}.…
Question Number 130301 by sarahvalencia last updated on 24/Jan/21 Answered by benjo_mathlover last updated on 24/Jan/21 $$\left(\mathrm{2}\right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} }\:\Rightarrow\:\int\:\mathrm{y}^{\mathrm{2}} \mathrm{dy}−\int\mathrm{x}^{\mathrm{2}} \mathrm{dx}=\mathrm{C} \\ $$$$\:\mathrm{y}^{\mathrm{3}} −\mathrm{x}^{\mathrm{3}} \:=\:\mathrm{3C}\:;\:\mathrm{y}^{\mathrm{3}}…
Question Number 64762 by Lontum Hans-Sandys last updated on 21/Jul/19 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{3x}^{\mathrm{2}} \right.} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{express}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{g}\left(\left(\mathrm{x}\right)\:\mathrm{dx}.\right. \\ $$ Commented by mathmax by abdo…
Question Number 130296 by sumit Singh last updated on 24/Jan/21 $$\int\left({x}^{\mathrm{2}} /\mathrm{2}+{x}\right){dx} \\ $$ Commented by EDWIN88 last updated on 24/Jan/21 $$\int\:\left(\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{x}\right)\mathrm{dx}\:\mathrm{or}\:\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}+\mathrm{x}}\:\mathrm{dx}\:? \\…