Question Number 122877 by bemath last updated on 20/Nov/20 $$\:\:\int\:\left(\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\right)^{\mathrm{2}} \:{dx}\:? \\ $$ Commented by liberty last updated on 20/Nov/20 $$\:{let}\:{u}\:=\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\:\Rightarrow{x}\:=\:\mathrm{sin}\:{u}\: \\ $$$$\Rightarrow\:{dx}\:=\:\mathrm{cos}\:{u}\:{du}\:…
Question Number 122867 by bemath last updated on 20/Nov/20 Answered by som(math1967) last updated on 20/Nov/20 $$\mathrm{I}=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{\sqrt{\mathrm{cosx}}\mathrm{dx}}{\:\sqrt{\mathrm{cosx}}+\sqrt{\mathrm{sinx}}} \\ $$$$\mathrm{again}\:\mathrm{I}=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{\sqrt{\mathrm{cos}\left(\frac{\pi}{\mathrm{2}}−\mathrm{x}\right)}\mathrm{dx}}{\:\sqrt{\mathrm{cos}\left(\frac{\pi}{\mathrm{2}}−\mathrm{x}\right)}+\sqrt{\mathrm{sin}\left(\frac{\pi}{\mathrm{2}}−\mathrm{x}\right)}} \\ $$$$=\underset{\mathrm{0}}…
Question Number 57325 by turbo msup by abdo last updated on 02/Apr/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{ln}\left(\mathrm{1}+{sinx}\right)}{{sinx}}{dx} \\ $$ Commented by Abdo msup. last updated on 05/Apr/19…
Question Number 57324 by turbo msup by abdo last updated on 02/Apr/19 $${we}\:{want}\:{to}\:{find}\:{the}\:{vslue}\:{of} \\ $$$${I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:{let} \\ $$$${A}=\int\int_{{W}} \frac{{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{xy}\right)}{dxdy} \\ $$$${with}\:{W}=\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} \\…
Question Number 57323 by turbo msup by abdo last updated on 02/Apr/19 $${calculate}\:\int\int_{{D}} \:\:\frac{{x}+{y}}{\mathrm{3}+\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }}{dxdy} \\ $$$${with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{2}\right. \\ $$$$\left.{and}\:{x}\geqslant\mathrm{0}\:,{y}\geqslant\mathrm{0}\right\} \\ $$…
Question Number 57321 by turbo msup by abdo last updated on 02/Apr/19 $${calculate}\:\int\int_{{D}} \left({x}−{y}\right)\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy} \\ $$$${with}\:{D}\:=\left\{\:\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{2}\:{and}\:{x}\geqslant\mathrm{0}\right\} \\ $$ Commented by…
Question Number 57320 by turbo msup by abdo last updated on 02/Apr/19 $${calculate}\:\int\int_{{D}} {xy}\:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \:{dxdy} \\ $$$${with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\:{and}\right. \\ $$$$\left.\mathrm{1}\leqslant{y}\leqslant\mathrm{3}\right\} \\ $$ Commented…
Question Number 122853 by rs4089 last updated on 20/Nov/20 Commented by Dwaipayan Shikari last updated on 20/Nov/20 $${y}\:\:\:\bigtriangleup{y}\:\bigtriangleup^{\mathrm{2}} {y} \\ $$$$\mathrm{2} \\ $$$$\:\:\:\:\:\:\mathrm{3} \\ $$$$\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}…
Question Number 57319 by turbo msup by abdo last updated on 02/Apr/19 $${calculate}\:\int\int_{{D}} \:{e}^{{x}−{y}} \:{dxdy} \\ $$$${with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} \:/\mid{x}\mid<\mathrm{1}\:{and}\:\mathrm{0}\leqslant{y}\leqslant\mathrm{1}\right\} \\ $$ Commented by maxmathsup by imad…
Question Number 188384 by universe last updated on 28/Feb/23 $$\:\:\: \\ $$$$\:\:\:\mathrm{if}\:\:\:\:\int_{\mathrm{0}} ^{\infty} {e}^{−{ax}} {dx}\:\:=\:\:\frac{\mathrm{1}}{{a}} \\ $$$$\:\:\:\:\:\:\:\:{show}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} {e}^{−{ax}} \:{x}^{{n}} {dx}\:\:=\:\:\frac{{n}!}{{a}^{{n}+\mathrm{1}} } \\ $$ Answered…