Question Number 221483 by Nicholas666 last updated on 06/Jun/25 $$ \\ $$$$\:\:\:\:{I}\left(\alpha\right)\:=\:\int\int\int_{\:\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \:\frac{\mathrm{ln}\left(\mathrm{1}\:+\:\alpha\left({xy}\:+\:{yz}\:+\:{zx}\right)\right)}{\mathrm{1}\:−\:{xyz}\:}\:{dxdydz}\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{for}\:\alpha\:\in\:\left(\mathrm{0},\mathrm{1}\right) \\ $$$$ \\ $$ Commented by MrGaster last updated…
Question Number 221473 by wewji12 last updated on 06/Jun/25 Answered by MathematicalUser2357 last updated on 06/Jun/25 $$\mathrm{279}\pi \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221438 by Nicholas666 last updated on 05/Jun/25 $$ \\ $$$$\:\:\:\int_{\:\mathrm{1}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{ln}\:{x}\right)}{\mathrm{1}−\mathrm{2}{x}\:\mathrm{cos}\:\theta\:+\:{x}^{\mathrm{2}} }\:{dx}\:;\:\mathrm{for}\:\mathrm{all}\:\theta\:\in\:\left(−\pi\:,\:\pi\right)\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221435 by wewji12 last updated on 05/Jun/25 $$\mathrm{g};\mathbb{R}\rightarrow\mathbb{R}\:,\:\mathrm{g}\in\mathcal{C}^{\omega} \:\mathrm{at}\:\mathbb{R}\:\mathrm{space} \\ $$$$\:\mathrm{evauate}\: \\ $$$$−\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:{y}\centerdot\mathrm{g}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\mathrm{d}{x}\mathrm{d}{y} \\ $$$$\mathrm{when}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{z}^{\mathrm{2}}…
Question Number 221444 by Tawa11 last updated on 05/Jun/25 Commented by Tawa11 last updated on 05/Jun/25 In the ∆ABC |AB|=|BC|=|AC|=K, Area of the shaded ∆…
Question Number 221430 by pronation last updated on 05/Jun/25 Answered by wewji12 last updated on 05/Jun/25 $$\mathrm{Automorphism}\:\mathrm{group}..?? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221447 by Nicholas666 last updated on 05/Jun/25 $$ \\ $$$$\:\:\:\:\mathrm{if}\:\:\:\:\:\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\:\left({x}\:+\:{r}_{{i}} \right)\:\equiv\:\underset{{j}=\mathrm{0}} {\overset{{n}} {\sum}}\:{a}_{{j}} {x}^{{n}−{i}} \: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\:; \\ $$$$\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{tan}^{−\mathrm{1}}…
Question Number 221416 by wewji12 last updated on 04/Jun/25 $$\mathrm{ex3}. \\ $$$$\mathrm{prove} \\ $$$${f}^{\left({n}\right)} \left(\alpha\right)=\frac{{n}!}{\mathrm{2}\pi\boldsymbol{{i}}}\:\oint_{\:\partial{S}} \:\frac{{f}\left({z}\right)}{\left({z}−\alpha\right)^{{n}+\mathrm{1}} }\:\mathrm{d}{z} \\ $$$$\mathrm{ex4}. \\ $$$$\mathrm{Let}\:{z}_{\mathrm{0}} \:\mathrm{be}\:\mathrm{any}\:\mathrm{point}\:\mathrm{interior}\:\mathrm{to}\:\mathrm{a}\:\mathrm{positively} \\ $$$$\mathrm{oriented}\:\mathrm{simple}\:\mathrm{closed}\:\mathrm{contour}\:\mathcal{C} \\…
Question Number 221417 by leromain last updated on 04/Jun/25 $${Let}\:\:{S}\:{be}\:{delimited}\:{by}\:{the}\:{equations}\: \\ $$$${x}=\mathrm{0};\:{y}=\mathrm{0}\:;\:{z}=\mathrm{0}\:{and}\:{x}+{y}+{z}=\mathrm{0} \\ $$$${Find}\:{the}\:{flux}\:{of}\:{vector}\:{field}\: \\ $$$${V}\left({x},{y},{z}\right)=\left({x},{y},{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\:{through}\:{S} \\ $$ Terms of Service Privacy Policy…
Question Number 221413 by BHOOPENDRA last updated on 04/Jun/25 Answered by mr W last updated on 05/Jun/25 $${x}=\mathrm{4}\:\mathrm{cos}\:\theta \\ $$$${y}=\mathrm{2}\:\mathrm{sin}\:\theta \\ $$$${x}+{y}=\mathrm{2}\left(\mathrm{2}\:\mathrm{cos}\:\theta+\mathrm{sin}\:\theta\right)=\mathrm{2}\sqrt{\mathrm{5}}\:\mathrm{sin}\:\left(\theta+\mathrm{tan}^{−\mathrm{1}} \mathrm{2}\right) \\ $$$$\left({x}+{y}\right)_{{min}}…