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Author: Tinku Tara

H-0-4-tanx-dx-

Question Number 6439 by sanusihammed last updated on 27/Jun/16 $${H}\:=\:\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{4}}} \sqrt{{tanx}}\:{dx}\: \\ $$ Commented by Temp last updated on 27/Jun/16 $$\int\sqrt{\mathrm{tan}{x}}{dx}\:\mathrm{is}\:\mathrm{difficult}\:\mathrm{to}\:\mathrm{solve}. \\ $$ Commented…

sin-1-x-x-3-dx-

Question Number 137508 by EDWIN88 last updated on 03/Apr/21 $$\int\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{1}}{{x}}\right)}{{x}^{\mathrm{3}} }\:{dx}\:=? \\ $$ Answered by liberty last updated on 03/Apr/21 $${L}=\int\:\frac{\mathrm{1}}{{x}}\mathrm{sin}\:\left(\frac{\mathrm{1}}{{x}}\right)\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\:{dx} \\ $$$${let}\:{t}\:=\:\frac{\mathrm{1}}{{x}}\:\Rightarrow−{dt}\:=\:\frac{{dx}}{{x}^{\mathrm{2}} }…

Question-6436

Question Number 6436 by sanusihammed last updated on 27/Jun/16 Answered by Rasheed Soomro last updated on 28/Jun/16 $${P}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +{ax}+{b} \\ $$$${x}−\mathrm{2}\:{is}\:{factor}\:{of}\:{P}\left({x}\right)\:{means}\:{if}\:{P}\left({x}\right)\:{is}\:{divided} \\ $$$${by}\:{x}−\mathrm{2}\:,\:{the}\:{remainder}\:{will}\:{be}\:\mathrm{0} \\…

advanced-calculus-prove-that-0-1-ln-x-ln-1-x-1-x-dx-13-8-3-pi-2-4-ln-2-

Question Number 137501 by mnjuly1970 last updated on 03/Apr/21 $$\:\:\:\:\:\:\:….{advanced}\:….\:{calculus}…. \\ $$$$\:\:{prove}\:{that}:: \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right).{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}}{dx}=\frac{\mathrm{13}}{\mathrm{8}}\zeta\left(\mathrm{3}\right)−\frac{\pi^{\mathrm{2}} }{\mathrm{4}}{ln}\left(\mathrm{2}\right)…. \\ $$ Answered by Ñï= last updated on…

An-oil-can-is-to-be-made-in-form-of-a-right-circular-cylinder-that-be-inscribed-in-a-sphere-of-radius-R-obtain-the-maximum-volume-of-the-can-

Question Number 6430 by sanusihammed last updated on 27/Jun/16 $${An}\:{oil}\:{can}\:{is}\:{to}\:{be}\:{made}\:{in}\:{form}\:{of}\:{a}\:{right}\:{circular}\:{cylinder}\:{that}\:{be} \\ $$$${inscribed}\:{in}\:{a}\:{sphere}\:{of}\:{radius}\:{R}.\:{obtain}\:{the}\:{maximum}\: \\ $$$${volume}\:{of}\:{the}\:{can}. \\ $$ Commented by sanusihammed last updated on 27/Jun/16 $${Thanks}\:{so}\:{much}\:{sir}.\: \\…

Question-71960

Question Number 71960 by TawaTawa last updated on 22/Oct/19 Answered by mind is power last updated on 22/Oct/19 $$\Sigma\frac{\mathrm{1}+\mathrm{a}}{\mathrm{1}−\mathrm{a}}=\Sigma\left(−\mathrm{1}+\frac{\mathrm{2}}{\mathrm{1}−\mathrm{a}}\right)=\Sigma−\mathrm{1}+\Sigma\frac{\mathrm{2}}{\mathrm{1}−\mathrm{a}} \\ $$$$\frac{\mathrm{p}'\left(\mathrm{x}\right)}{\mathrm{p}\left(\mathrm{x}\right)}=\underset{\mathrm{a}\in\mathrm{Root}\left(\mathrm{p}\right)} {\sum}\frac{\mathrm{1}}{\mathrm{x}−\mathrm{a}} \\ $$$$\Rightarrow\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{3}}…