Question Number 4196 by Rasheed Soomro last updated on 31/Dec/15 $$\:\:\mathrm{Q}#\mathrm{4140}\:\mathrm{is}\:\mathrm{again}\:\mathrm{asked}\:\mathrm{with}\:\mathrm{following}\:\mathrm{changes}: \\ $$$$\boldsymbol{\mathrm{a}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{b}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{b}}\right), \\ $$$$\boldsymbol{\mathrm{b}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{c}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{c}}\right), \\ $$$$\boldsymbol{\mathrm{c}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{d}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{d}}\right),\: \\ $$$$\boldsymbol{\mathrm{d}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{a}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{a}}\right), \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{a}}',\boldsymbol{\mathrm{b}}',\boldsymbol{\mathrm{c}}'\:\mathrm{and}\:\boldsymbol{\mathrm{d}}'\:\mathrm{are}\:\mathrm{midpoints}\:\mathrm{of}\:\mathrm{line} \\ $$$$\mathrm{segments}\:\boldsymbol{\mathrm{ab}},\:\boldsymbol{\mathrm{bc}},\:\boldsymbol{\mathrm{cd}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{da}}\:\mathrm{respectively}. \\ $$…
Question Number 135257 by leena12345 last updated on 11/Mar/21 $$\int{t}^{\mathrm{7}} {ln}\left({t}\right){dt} \\ $$ Commented by leena12345 last updated on 11/Mar/21 $${help} \\ $$ Answered by…
Question Number 135259 by leena12345 last updated on 11/Mar/21 $$\int\left({x}^{\mathrm{2}} +\mathrm{3}{x}\right)\mathrm{cos}\:\left({x}\right){dx} \\ $$ Answered by Ar Brandon last updated on 11/Mar/21 $$\mathcal{I}=\int\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3x}\right)\mathrm{cosxdx} \\ $$$$\:\:\:=\left(\mathrm{x}^{\mathrm{2}}…
Question Number 135253 by otchereabdullai@gmail.com last updated on 11/Mar/21 Commented by mr W last updated on 11/Mar/21 $$\angle{YXZ}=\mathrm{90}°\:\Rightarrow{YX}=\sqrt{\mathrm{5}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }=\mathrm{4} \\ $$$${area}\:{of}\:\Delta{XYZ}=\frac{{YX}×{XZ}}{\mathrm{2}}=\frac{{YZ}×{XN}}{\mathrm{2}} \\ $$$$\Rightarrow{XN}=\frac{\mathrm{4}×\mathrm{3}}{\mathrm{5}}=\frac{\mathrm{12}}{\mathrm{5}} \\…
Question Number 135252 by mnjuly1970 last updated on 11/Mar/21 $$\:\:\:\:\:\:\:\:\:….{advanced}\:\:\:\:{calculus}…. \\ $$$$\:\:\:\:{first}\:{prove}\:{that}::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx}=\frac{−\mathrm{5}}{\mathrm{8}}\:\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:{then}\:{conclude}\:{that}:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}_{\mathrm{2}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)}{{x}}{dx}=\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{4}}…
Question Number 135254 by 0731619177 last updated on 11/Mar/21 Answered by Dwaipayan Shikari last updated on 11/Mar/21 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \left(\frac{{e}^{−{ax}^{\mathrm{2}} } −{e}^{−{bx}^{\mathrm{2}} } }{{x}}\right)^{\mathrm{2}} {dx}…
Question Number 69715 by Mikaell last updated on 26/Sep/19 $$\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{e}^{{x}} {dx} \\ $$ Answered by mind is power last updated on 27/Sep/19 $$\int\frac{{x}^{\mathrm{2}}…
Question Number 4176 by Yozzii last updated on 31/Dec/15 Commented by Yozzii last updated on 31/Dec/15 $${If}\:{it}'{s}\:{hard}\:{to}\:{read},\:{the}\:{info} \\ $$$${reads}\:{x}\geqslant{b}>\mathrm{0}. \\ $$ Commented by prakash jain…
Question Number 69710 by ahmadshahhimat775@gmail.com last updated on 26/Sep/19 Commented by mathmax by abdo last updated on 27/Sep/19 $${we}\:{have}\:{x}^{\mathrm{2}} −\mathrm{6}{x}\:+\mathrm{5}\:={x}^{\mathrm{2}} −{x}\:−\mathrm{5}\left({x}−\mathrm{1}\right)={x}\left({x}−\mathrm{1}\right)−\mathrm{5}\left({x}−\mathrm{1}\right) \\ $$$$=\left({x}−\mathrm{1}\right)\left({x}−\mathrm{5}\right) \\ $$$$\Rightarrow{lim}_{{x}\rightarrow\mathrm{1}}…
Question Number 135246 by ajfour last updated on 11/Mar/21 Commented by ajfour last updated on 11/Mar/21 $${Who}\:{does}\:{this}\:{person},\:{expect} \\ $$$${to}\:{meet}? \\ $$$$\left.{a}\left.\right){male}\:\:{b}\right){female} \\ $$ Commented by…