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Author: Tinku Tara

x-1-x-dx-

Question Number 82566 by jagoll last updated on 22/Feb/20 $$\int\:\sqrt{\frac{{x}+\mathrm{1}}{{x}}}\:{dx}\:=\:? \\ $$ Commented by mathmax by abdo last updated on 22/Feb/20 $${let}\:{I}=\int\sqrt{\frac{{x}+\mathrm{1}}{{x}}}{dx}\:{changement}\:\sqrt{\frac{{x}+\mathrm{1}}{{x}}}={t}\:{give}\:\frac{{x}+\mathrm{1}}{{x}}={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${x}+\mathrm{1}\:={xt}^{\mathrm{2}}…

cot-2-x-3-dx-

Question Number 17030 by tawa tawa last updated on 29/Jun/17 $$\int\:\mathrm{cot}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{3}} \right)\:\mathrm{dx} \\ $$ Commented by Arnab Maiti last updated on 03/Jul/17 $$\mathrm{How}\:\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:?\:\int\mathrm{x}^{\mathrm{2}} \mathrm{cot}^{\mathrm{2}}…

Use-gamma-function-to-prove-i-0-pi-4-sin-4-x-2x-dx-3-4-192-ii-0-pi-6-cos-4-3-sin-2-6-5pi-192-

Question Number 82560 by niroj last updated on 22/Feb/20 $$\:\boldsymbol{\mathrm{U}}\mathrm{se}\:\mathrm{gamma}\:\mathrm{function}\:\mathrm{to}\:\mathrm{prove} \\ $$$$\:\:\left(\mathrm{i}\right)\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \boldsymbol{\mathrm{sin}}^{\mathrm{4}} \boldsymbol{\mathrm{x}}\:\mathrm{2}\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}\:=\:\frac{\mathrm{3}\boldsymbol{\pi}−\mathrm{4}}{\mathrm{192}}. \\ $$$$\:\:\left(\mathrm{ii}\right)\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \:\boldsymbol{\mathrm{cos}}^{\mathrm{4}} \mathrm{3}\boldsymbol{\theta}\:\mathrm{sin}^{\mathrm{2}} \mathrm{6}\theta\:=\:\frac{\mathrm{5}\pi}{\mathrm{192}}. \\ $$ Answered by…

a-polynomial-gives-a-remainder-of-x-1-when-divided-by-x-2-and-a-remainder-of-1-when-divided-by-x-1-what-is-the-remainder-when-the-polynomial-divided-by-x-2-x-1-

Question Number 82561 by jagoll last updated on 22/Feb/20 $${a}\:{polynomial}\:{gives}\:{a}\:{remainder} \\ $$$${of}\:−{x}−\mathrm{1}\:{when}\:{divided}\:{by}\:{x}^{\mathrm{2}.} \\ $$$${and}\:\:{a}\:{remainder}\:{of}\:−\mathrm{1}\:{when}\: \\ $$$${divided}\:{by}\:{x}−\mathrm{1}\:.\:{what}\:{is}\:{the}\: \\ $$$${remainder}\:{when}\:{the}\:{polynomial} \\ $$$${divided}\:{by}\:{x}^{\mathrm{2}} \left({x}−\mathrm{1}\right)\:? \\ $$ Answered by…

Question-148092

Question Number 148092 by puissant last updated on 25/Jul/21 Answered by Olaf_Thorendsen last updated on 25/Jul/21 $$\mathrm{R}\:\mathrm{est}\:\mathrm{le}\:\mathrm{rayon}\:\mathrm{du}\:\mathrm{cercle}. \\ $$$$\mathrm{O}\:\mathrm{est}\:\mathrm{le}\:\mathrm{centre}\:\mathrm{du}\:\mathrm{cercle}. \\ $$$$\mathrm{B}\begin{pmatrix}{\mathrm{R}}\\{\mathrm{R}}\end{pmatrix},\:\mathrm{C}\begin{pmatrix}{\mathrm{R}}\\{\mathrm{R}−\mathrm{15}}\end{pmatrix} \\ $$$$\mathrm{Aire}_{\mathrm{ABC}} \:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{AB}×\mathrm{AC} \\…