Question Number 10790 by Nur450737 last updated on 25/Feb/17 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\mathrm{sin}\:{x}}\:{dx} \\ $$ Answered by bahmanfeshki last updated on 26/Feb/17 $$\sqrt{\mathrm{sin}\:{x}}={t} \\ $$$${t}^{\mathrm{2}} =\mathrm{sin}\:{x}\Rightarrow\mathrm{cos}\:{x}=\sqrt{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 10789 by niraj last updated on 25/Feb/17 $$\left(\mathrm{2}+\mathrm{3}{i}\right){x}^{\mathrm{2}} −\left(\mathrm{3}−\mathrm{2}{i}\right){y}=\mathrm{2}{x}−\mathrm{3}{y}+\mathrm{5}{i} \\ $$ Answered by sandy_suhendra last updated on 25/Feb/17 $$\left(\mathrm{2}+\mathrm{3i}\right)\mathrm{x}^{\mathrm{2}} −\mathrm{3y}+\mathrm{2iy}=\mathrm{2x}−\mathrm{3y}+\mathrm{5i} \\ $$$$\Rightarrow\:\left(\mathrm{2}+\mathrm{3i}\right)\mathrm{x}^{\mathrm{2}} =\mathrm{2x}…
Question Number 10788 by okhema last updated on 25/Feb/17 $${factorise}\:{the}\:{expression}\:{sin}\mathrm{4}{x}−{sinx} \\ $$ Answered by argemiroQR last updated on 26/Feb/17 $${sin}\left(\mathrm{3}{x}+{x}\right)−{sinx}= \\ $$$${sin}\mathrm{3}{xcosx}+{cos}\mathrm{3}{xsinx}−{sinx}= \\ $$$${cosx}\left(\mathrm{3}{sinx}−\mathrm{4}{sin}^{\mathrm{3}} {x}\right)+\left({cos}^{\mathrm{3}}…
Question Number 10787 by Saham last updated on 25/Feb/17 Commented by sandy_suhendra last updated on 25/Feb/17 $$\mathrm{is}\:\mathrm{that}\:\mathrm{P}=\mathrm{P}_{\mathrm{0}} \left[\frac{\mathrm{T}_{\mathrm{0}} }{\mathrm{T}_{\mathrm{0}} +\mathrm{Kz}}\right]^{\frac{\mathrm{g}}{\mathrm{KR}}} \:? \\ $$ Commented by…
Question Number 141856 by rs4089 last updated on 24/May/21 Answered by TheSupreme last updated on 24/May/21 $${x}=\rho{sin}\left(\varphi\right){cos}\left(\theta\right) \\ $$$${y}=\rho{sin}\left(\varphi\right){sin}\left(\theta\right) \\ $$$${z}=\rho{cos}\left(\theta\right) \\ $$$${det}\mid{J}\mid=\rho^{\mathrm{2}} {sin}\left(\varphi\right) \\…
Question Number 76323 by aliesam last updated on 26/Dec/19 Commented by mind is power last updated on 27/Dec/19 $$\mathrm{I}_{\mathrm{n}} =\int\mathrm{cos}^{\mathrm{n}} \left(\mathrm{x}\right)\mathrm{e}^{\mathrm{ax}} \mathrm{dx} \\ $$$$\mathrm{by}\:\mathrm{part} \\…
Question Number 141859 by iloveisrael last updated on 24/May/21 $$\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{4}{e}^{−{x}^{\mathrm{2}} } }{\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\: \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 141858 by gsk2684 last updated on 24/May/21 Commented by gsk2684 last updated on 24/May/21 $${solution}\:{please} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 141855 by rs4089 last updated on 24/May/21 Answered by TheSupreme last updated on 24/May/21 $${E}=\left\{\left({x},{y}\right)\mid{y}<{x}<{a}\:\vee\:\mathrm{0}<{y}<{a}\right\} \\ $$$${E}^{\mathrm{1}} =\left\{\left(\rho,\theta\right)\mid\:\mathrm{0}<\rho<{a},\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{4}}\right\} \\ $$$${det}\mid{J}\mid=\rho \\ $$$$\int_{\mathrm{0}} ^{{a}}…
Question Number 76317 by Master last updated on 26/Dec/19 Commented by john santu last updated on 26/Dec/19 $$\int{e}^{{xlnx}} \:{dx}.\:{with}\:{integration}\:{by}\:{part} \\ $$$${u}={e}^{{xlnx}} \rightarrow{du}=\left({lnx}+\mathrm{1}\right){e}^{{xlnx}} .\:{dv}={dx}\: \\ $$$${I}={xe}^{{xlnx}}…