Menu Close

Author: Tinku Tara

a-b-2-a-2-b-2-2ab-a-b-c-2-a-2-b-2-c-2-2ab-2bc-2ca-a-b-c-d-2-a-1-a-2-a-n-2-Derive-a-formula-or-give-a-technique-

Question Number 2196 by Rasheed Soomro last updated on 08/Nov/15 $$\left({a}+{b}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{2}{ab} \\ $$$$\left({a}+{b}+{c}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\mathrm{2}{ab}+\mathrm{2}{bc}+\mathrm{2}{ca} \\ $$$$\left({a}+{b}+{c}+{d}\right)^{\mathrm{2}} =? \\ $$$$\left({a}_{\mathrm{1}}…

n-1-sinn-n-3-

Question Number 133264 by Dwaipayan Shikari last updated on 20/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sinn}}{{n}^{\mathrm{3}} } \\ $$ Commented by Dwaipayan Shikari last updated on 20/Feb/21 $${I}\:{have}\:{found}\:\frac{\mathrm{1}}{\mathrm{12}}−\frac{\pi}{\mathrm{4}}+\frac{\pi^{\mathrm{2}}…

Let-J-0-f-x-x-1-2-dx-where-f-is-any-function-for-which-the-integral-exists-Show-that-J-0-x-2-f-x-x-1-2-dx-0-5-0-1-x-2-f-x-x-1-2-dx-0-f-u-2-du-

Question Number 2186 by Yozzi last updated on 07/Nov/15 $${Let}\:{J}=\int_{\mathrm{0}} ^{\infty} {f}\left(\left({x}−{x}^{−\mathrm{1}} \right)^{\mathrm{2}} \right){dx}\:{where}\:{f}\:{is} \\ $$$${any}\:{function}\:{for}\:{which}\:{the}\:{integral} \\ $$$${exists}.\:{Show}\:{that} \\ $$$${J}=\int_{\mathrm{0}} ^{\infty} {x}^{−\mathrm{2}} {f}\left(\left({x}−{x}^{−\mathrm{1}} \right)^{\mathrm{2}} \right){dx}=\mathrm{0}.\mathrm{5}\int_{\mathrm{0}}…

Question-67719

Question Number 67719 by aliesam last updated on 30/Aug/19 Answered by mind is power last updated on 30/Aug/19 $$\Leftrightarrow\frac{{d}\left({y}+{x}\right)}{{dx}}+{x}\left({x}+{y}\right)={x}^{\mathrm{3}} \left({x}+{y}\right)^{\mathrm{5}} \\ $$$${let}\:{z}={y}+{x} \\ $$$$\Rightarrow\frac{{dz}}{{dx}}+{xz}={x}^{\mathrm{3}} {z}^{\mathrm{5}}…