Question Number 128688 by BHOOPENDRA last updated on 09/Jan/21 $${find}\:{the}\:{flux}\:{of}\:{the}\:{vector}\:{field} \\ $$$${F}={x}\hat {{i}}+{y}\hat {{j}}+\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{1}\:\hat {{k}}} \\ $$$${through}\:{outer}\:{side}\:{of}\:{hyper}−{boloide} \\ $$$${z}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{1}} \\ $$$${bounded}\:{by}\:{the}\:{planes}\:…
Question Number 128592 by BHOOPENDRA last updated on 09/Jan/21 $$\int\int\int_{{V}} \bigtriangledown×{F}\:{dV}\:{where}\:{F}=\left({x}+\mathrm{2}{y}\right)\hat {{i}}−\mathrm{3}{z}\hat {{j}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+{x}\hat {{k}} \\ $$$${and}\:{V}\:{is}\:{the}\:{closed}\:{region}\:{in}\:{first}\:{octant} \\ $$$${by}\:{the}\:{plane}\:\mathrm{2}{x}+\mathrm{2}{y}+\mathrm{2}{z}=\mathrm{4} \\ $$$$ \\ $$ Answered…
Question Number 128591 by BHOOPENDRA last updated on 09/Jan/21 $${verify}\:{the}\:{gauss}\:{divergence}\:{theorem} \\ $$$${f}=\left({x}^{\mathrm{2}} −{yz}\right)\hat {{i}}+\left({y}^{\mathrm{2}} −{zx}\right)\hat {\mathrm{j}}+\left({z}^{\mathrm{2}} −{xy}\right)\hat {{k}} \\ $$$${over}\:{the}\:{region}\:{R}\:{bounded}\:{by}\:{the}\: \\ $$$$ \\ $$$${parallelepiped}\:\mathrm{0}\leqslant{x}\leqslant{a},\mathrm{0}\leqslant{y}\leqslant{b}, \\…
Question Number 128282 by BHOOPENDRA last updated on 06/Jan/21 Answered by mr W last updated on 06/Jan/21 $${ellipse}\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{2}} }=\mathrm{1} \\ $$$${or} \\…
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Question Number 62517 by Tawa1 last updated on 22/Jun/19 Commented by $@ty@m last updated on 22/Jun/19 $${what}\:{is}\:{meant}\:{by}\:{BC}=\begin{pmatrix}{\mathrm{3}}\\{\mathrm{1}}\end{pmatrix}\: \\ $$$${pl}.\:{clarify}\:{this}\:{notation}. \\ $$ Commented by Prithwish sen…
Question Number 61258 by cesar.marval.larez@gmail.com last updated on 31/May/19 $$\boldsymbol{{C}}{alculate},\:{using}\:{cartesian}\:{coodinates},\:{the}\:{following} \\ $$$${integrals}: \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\int\int_{{D}} {dxdy}\:\:{being}\:\:{D}=\left\{\:\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}},{y}+{x}\leqslant\mathrm{1},{y}\geqslant\mathrm{0}\right\} \\ $$$$\left.\mathrm{2}\right)\:\int\int_{{D}} {x}^{\mathrm{3}} {ydxdy}\:\:{being}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}},{y}+{x}\leqslant\mathrm{1},{y}\geqslant\mathrm{0}\right\} \\ $$$$\left.\mathrm{3}\right)\:\int\int_{{D}}…
Question Number 126646 by sdfg last updated on 22/Dec/20 Commented by sdfg last updated on 22/Dec/20 $${please}\:{help} \\ $$ Answered by physicstutes last updated on…
Question Number 126572 by sdfg last updated on 22/Dec/20 Answered by liberty last updated on 22/Dec/20 $$\:\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid^{\mathrm{2}} =\:\mid\overset{\rightarrow} {{a}}\mid^{\mathrm{2}} +\mid\overset{\rightarrow} {{b}}\mid^{\mathrm{2}} +\mathrm{2}\mid\overset{\rightarrow} {{a}}\mid\mid\overset{\rightarrow}…
Question Number 192024 by Shlock last updated on 05/May/23 Answered by a.lgnaoui last updated on 05/May/23 $$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{shaded}}\:\boldsymbol{\mathrm{Area}}\:\boldsymbol{\mathrm{betwen}} \\ $$$$\left[\boldsymbol{\mathrm{y}}=\mathrm{0},\boldsymbol{\mathrm{y}}=\sqrt{\mathrm{25}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:−\mathrm{3}\:\:;\boldsymbol{\mathrm{y}}=\sqrt{\mathrm{4}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:}\right] \\ $$$$\int_{\mathrm{0}} ^{\mathrm{4}} \left(\sqrt{\mathrm{25}−\boldsymbol{\mathrm{x}}^{\mathrm{2}}…