Question Number 219346 by SdC355 last updated on 23/Apr/25 $$\int_{\mathrm{0}} ^{\:\infty} \mathrm{ln}\left({z}\right){e}^{−\mathrm{3}{z}} \mathrm{d}{z}=??? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219347 by SdC355 last updated on 23/Apr/25 $$\int_{\mathrm{0}} ^{\:\infty} \:{K}_{\mathrm{0}} \left({z}\right){e}^{−{kz}} \mathrm{d}{z}=??? \\ $$$${K}_{\nu} \left({z}\right)\:\mathrm{is}\:\mathrm{modified}\:\mathrm{Bessel}\:\mathrm{function} \\ $$ Answered by Nicholas666 last updated on…
Question Number 219340 by SdC355 last updated on 23/Apr/25 $$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)=−\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −\frac{{y}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −\frac{{z}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}}…
Question Number 219341 by alcohol last updated on 23/Apr/25 $$\int\frac{{dx}}{\mathrm{1}\:+\:{sin}^{\mathrm{3}} {x}\:+\:{cos}^{\mathrm{3}} {x}} \\ $$ Commented by Ghisom last updated on 23/Apr/25 $$\mathrm{simply}\:\mathrm{use}\:{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{decompose} \\ $$$$\mathrm{which}\:\mathrm{leads}\:\mathrm{to} \\…
Question Number 219343 by SdC355 last updated on 23/Apr/25 $$\int\int\int_{\:\mathrm{S}} \:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −{z}^{\mathrm{2}} } \:\mathrm{dA}=??? \\ $$ Answered by Nicholas666 last updated on 23/Apr/25 $$\mathrm{4}\pi{R}^{\mathrm{2}}…
Question Number 219336 by Spillover last updated on 23/Apr/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219337 by Spillover last updated on 23/Apr/25 Answered by mr W last updated on 23/Apr/25 Commented by mr W last updated on 23/Apr/25…
Question Number 219338 by SdC355 last updated on 23/Apr/25 $$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}=−{x}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{z}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}\left({u},{v}\right)=\begin{cases}{\left(\mathrm{2}+\mathrm{3sin}\left({u}\right)\right)\mathrm{cos}\left({v}\right)}\\{\left(\mathrm{2}+\mathrm{3sin}\left({v}\right)\right)\mathrm{sin}\left({u}\right)}\\{\mathrm{3cos}\left({u}\right)}\end{cases} \\ $$$${u}\in\left[\mathrm{0},\mathrm{2}\pi\right]\:,\:{v}\in\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$$$\int\int_{\:\boldsymbol{\mathcal{S}}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\overset{\rightarrow}…
Question Number 219403 by ea last updated on 23/Apr/25 Answered by mr W last updated on 24/Apr/25 Commented by mr W last updated on 24/Apr/25…
Question Number 219339 by Spillover last updated on 23/Apr/25 Answered by mr W last updated on 23/Apr/25 $$\alpha=\mathrm{45}°+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{tan}\:\alpha=\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{1}−\mathrm{1}×\frac{\mathrm{1}}{\mathrm{2}}}=\mathrm{3} \\ $$ Answered by…