Question Number 70602 by oyemi kemewari last updated on 06/Oct/19 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \mathrm{ln}\left(\sqrt{\mathrm{1}−\mathrm{x}}\:+\sqrt{\mathrm{1}+\mathrm{x}}\right)\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Oct/19 $${error}\:{in}\:{the}\:{question}\:{the}\:{function}\:{x}\rightarrow\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{1}+{x}}\:{is}\:{defined}\:{on}…
Question Number 136136 by BHOOPENDRA last updated on 19/Mar/21 Answered by mr W last updated on 19/Mar/21 $${a}=\frac{{F}}{{m}}=\frac{\mathrm{150}}{\mathrm{10}}=\mathrm{15}\:{m}/{s}^{\mathrm{2}} \\ $$$${at}\:{t}=\mathrm{12}\:{s}: \\ $$$${v}={at}=\mathrm{15}×\mathrm{12}=\mathrm{180}\:{m}/{s} \\ $$$${s}=\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{15}×\mathrm{12}^{\mathrm{2}}…
Question Number 5065 by gourav~ last updated on 07/Apr/16 $$\int\sqrt{\mathrm{16}{x}^{\mathrm{2}} +\mathrm{25}}\:\:{dx}\:=? \\ $$ Answered by Yozzii last updated on 08/Apr/16 $${Let}\:{x}=\frac{\mathrm{5}}{\mathrm{4}}{sinh}\theta\Rightarrow{dx}=\frac{\mathrm{5}}{\mathrm{4}}{cosh}\theta{d}\theta \\ $$$$\sqrt{\mathrm{16}{x}^{\mathrm{2}} +\mathrm{25}}=\sqrt{\mathrm{16}×\frac{\mathrm{25}}{\mathrm{16}}{sinh}^{\mathrm{2}} \theta+\mathrm{25}}…
Question Number 136138 by bramlexs22 last updated on 19/Mar/21 $${What}\:{is}\:{max}\:{and}\:{min}\:{value} \\ $$$${of}\:{y}=\mathrm{4}−{x}^{\mathrm{2}} −\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:? \\ $$ Answered by ajfour last updated on 19/Mar/21 $${let}\:\:\mathrm{1}−{x}^{\mathrm{2}} ={s}\geqslant\mathrm{0}…
Question Number 70601 by oyemi kemewari last updated on 06/Oct/19 $$\mathrm{prove}\:\mathrm{thst}\:\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \mathrm{f}\left(\mathrm{x}+\frac{\mathrm{1}}{×}\right)\frac{\mathrm{lnx}}{\mathrm{x}}\mathrm{dx}=\mathrm{0} \\ $$ Answered by mind is power last updated on 06/Oct/19 $${let}\:{x}=\frac{\mathrm{1}}{{y}}\Rightarrow{I}=\int_{\infty}…
Question Number 70598 by Shamim last updated on 06/Oct/19 $$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\Re\:\mathrm{and}\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}+\mathrm{c}}+\frac{\mathrm{b}^{\mathrm{2}} }{\mathrm{c}+\mathrm{a}}+\frac{\mathrm{c}^{\mathrm{2}} }{\mathrm{a}+\mathrm{b}}=\frac{\mathrm{12}}{\mathrm{a}+\mathrm{b}+\mathrm{c}} \\ $$$$,\:\frac{\mathrm{a}}{\mathrm{b}+\mathrm{c}}+\frac{\mathrm{b}}{\mathrm{a}+\mathrm{c}}+\frac{\mathrm{c}}{\mathrm{a}+\mathrm{b}}=\frac{\mathrm{4}}{\mathrm{3}}\:\mathrm{then}\:\mathrm{find}\:\mathrm{a}+\mathrm{b}+\mathrm{c}=? \\ $$ Answered by som(math1967) last updated on 06/Oct/19 $$\frac{{a}^{\mathrm{2}}…
Question Number 136132 by frc2crc last updated on 19/Mar/21 $${Find}\:{a}\:{series}\:{for}\:\frac{{x}^{\mathrm{2}} }{\mathrm{tanh}\:\left({x}\pi\right)\mathrm{tan}\:\left({x}\pi\right)} \\ $$ Answered by Dwaipayan Shikari last updated on 19/Mar/21 $${sinh}\left(\pi{x}\right)=\pi{x}\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{n}^{\mathrm{2}}…
Question Number 70596 by mathmax by abdo last updated on 06/Oct/19 $${caoculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{{cos}\left({sin}\left({x}^{\mathrm{2}} \right)\right)−\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated on…
Question Number 70597 by Maclaurin Stickker last updated on 06/Oct/19 $${solve} \\ $$$$\mathrm{cos}\:^{\mathrm{2}} \beta+\mathrm{cos}\:^{\mathrm{2}} \mathrm{3}\beta=\mathrm{1} \\ $$ Answered by Kunal12588 last updated on 08/Oct/19 $${cos}\:\mathrm{2}\alpha\:=\:\mathrm{2}{cos}^{\mathrm{2}}…
Question Number 70594 by mathmax by abdo last updated on 06/Oct/19 $${calculate}\:{by}\:{residus}\:{method}\:{the}\:{integral}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} } \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$ Commented by mathmax by abdo…