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0-x-1-x-2-sin-2-x-dx-

Question Number 126904 by Mustafa2020 last updated on 25/Dec/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}}{\mathrm{1}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by mindispower last updated on 25/Dec/20 $$\geqslant\Sigma\int_{\mathrm{2}{k}\pi} ^{\mathrm{2}{k}\pi+\frac{\pi}{\mathrm{6}}}…

lim-n-1-n-1-1-n-2-1-n-3-1-2n-

Question Number 126886 by SOMEDAVONG last updated on 25/Dec/20 $$\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{3}}\:+….+\:\frac{\mathrm{1}}{\mathrm{2n}}\right) \\ $$ Answered by Dwaipayan Shikari last updated on 25/Dec/20 $$\frac{\mathrm{1}}{{n}}\left(\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{{n}}}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}}{{n}}}+….+\frac{\mathrm{1}}{\mathrm{1}+\frac{{n}}{{n}}}\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{1}+\frac{{r}}{{n}}}…

x-2-4-x-dx-

Question Number 192406 by josemate19 last updated on 17/May/23 $$\int\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}{{x}}\:{dx}??? \\ $$ Answered by mehdee42 last updated on 17/May/23 $${x}=\mathrm{2}{chu}\Rightarrow{dx}=\mathrm{2}{shudu} \\ $$$$\Rightarrow{I}=\mathrm{2}\int\:\frac{{sh}^{\mathrm{2}} {u}}{{chu}}\:{du}\:=\mathrm{2}\int\:\left({chu}−\frac{\mathrm{1}}{{chu}}\:\right){du} \\…

Give-the-function-x-2-7x-8-0-have-two-roots-x-1-and-x-2-No-solving-the-function-Find-x-1-3-x-2-2023-

Question Number 192390 by TUN last updated on 16/May/23 $${Give}\:{the}\:{function}: \\ $$$${x}^{\mathrm{2}} −\mathrm{7}{x}−\mathrm{8}=\mathrm{0} \\ $$$${have}\:{two}\:{roots}\:{x}_{\mathrm{1}\:} {and}\:{x}_{\mathrm{2}} \\ $$$${No}\:{solving}\:{the}\:{function}\: \\ $$$${Find}:\:{x}_{\mathrm{1}} ^{\mathrm{3}} +{x}_{\mathrm{2}} +\mathrm{2023} \\ $$…

Question-126848

Question Number 126848 by mohammad17 last updated on 24/Dec/20 Answered by mathmax by abdo last updated on 24/Dec/20 $$\mid\mathrm{z}−\mathrm{1}+\mathrm{i}\mid=\mathrm{1}\:\:\:\mathrm{put}\:\mathrm{z}=\mathrm{x}+\mathrm{iy}\:\Rightarrow \\ $$$$\mid\mathrm{z}−\mathrm{1}+\mathrm{i}\mid=\mid\mathrm{x}+\mathrm{iy}−\mathrm{1}+\mathrm{i}\mid=\mid\mathrm{x}−\mathrm{1}+\mathrm{i}\left(\mathrm{y}+\mathrm{1}\right)\mid=\sqrt{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \:+\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mid\mathrm{z}−\mathrm{1}+\mathrm{i}\mid=\mathrm{1}\:\Rightarrow\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}}…