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S-F-dS-F-yze-1-xze-2-xye-3-S-x-y-z-2-v-sin-u-sin-2piv-v-cos-u-2-v-sin-u-cos-2piv-2v-2-

Question Number 199736 by MathedUp last updated on 08/Nov/23 $$\int\int_{\:\boldsymbol{\mathcal{S}}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\hat {\boldsymbol{\mathrm{S}}} \\ $$$$\hat {\boldsymbol{\mathrm{F}}}=−{yz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −{xz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xy}\boldsymbol{\mathrm{e}}_{\mathrm{3}} \: \\ $$$$\hat {\boldsymbol{\mathrm{S}}};\:\begin{pmatrix}{\hat {{x}}}\\{\hat…

Question-199738

Question Number 199738 by sonukgindia last updated on 08/Nov/23 Answered by AST last updated on 08/Nov/23 $$\frac{{sin}\left({x}\right)}{{DB}}=\frac{{sin}\left(\alpha\right)}{{BC}};\frac{{sin}\left(\mathrm{2}{x}\right)}{{BE}={DB}}=\frac{{sinCEB}={sin}\left(\mathrm{90}+{x}\right)}{{BC}} \\ $$$$\Rightarrow\frac{{DB}}{{BC}}=\frac{{sin}\left({x}\right)}{{sin}\left(\alpha\right)}=\frac{{sin}\left(\mathrm{2}{x}\right)}{{sin}\left(\mathrm{90}+{x}\right)} \\ $$$$\Rightarrow{sin}\left(\alpha\right)=\frac{{sin}\left({x}\right)\left[{sin}\mathrm{90}{cosx}\right]}{\mathrm{2}{sinxcosx}}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow\alpha=\mathrm{30}° \\ $$ Commented by…

Question-199753

Question Number 199753 by sonukgindia last updated on 08/Nov/23 Answered by MM42 last updated on 09/Nov/23 $${let}\:\::\:\:{f}={xsinx}+{cosx}\:\:\&\:\:{g}={xcosx}+{sinx} \\ $$$${f}={g}\:\:\overset{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}} {\Rightarrow}\:{x}=\mathrm{1}\:,\frac{\pi}{\mathrm{4}} \\ $$$$\Rightarrow{s}=\mid\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \left({f}−{g}\right){dx}\mid+\mid\int_{\frac{\pi}{\mathrm{4}}} ^{\mathrm{1}}…

Question-199719

Question Number 199719 by sonukgindia last updated on 08/Nov/23 Answered by witcher3 last updated on 08/Nov/23 $$\mathrm{I}_{\mathrm{a}} =\mathrm{I}_{\mathrm{b}} \\ $$$$\mathrm{I}_{\mathrm{a}} =\int_{\mathrm{0}} ^{\pi} \mathrm{e}^{\mathrm{sin}\left(\mathrm{x}\right)} \mathrm{cos}\left(\mathrm{cos}\left(\mathrm{x}\right)\right)\mathrm{dx}+\int_{\pi} ^{\mathrm{2}\pi}…

Question-199666

Question Number 199666 by sonukgindia last updated on 07/Nov/23 Answered by witcher3 last updated on 07/Nov/23 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{x}^{\mathrm{a}} }{\mathrm{1}+\mathrm{x}^{\mathrm{b}} }\mathrm{dx}\:\mathrm{x}\rightarrow\mathrm{0}\:\frac{\mathrm{x}^{\mathrm{a}} }{\mathrm{1}+\mathrm{x}^{\mathrm{b}} }\sim\mathrm{x}^{\mathrm{a}} \:\mathrm{cv}\:\mathrm{if}\:\mathrm{only}\:\mathrm{if}?\mathrm{a}>−\mathrm{1}..\mathrm{true} \\…

Can-you-help-me-pls-Evaluate-S-F-dS-Parametric-Surface-S-u-v-2-sin-u-cos-v-e-1-2-sin-u-sin-v-e-2-cos-v-u-e-3-Vector-Field-F-x-y-xe-1-ye-2-ze

Question Number 199686 by MathedUp last updated on 07/Nov/23 $${Can}\:{you}\:{help}\:{me}..???\:{pls}…. \\ $$$$\: \\ $$$$\: \\ $$$$\mathrm{Evaluate}\:\int\int_{\:\boldsymbol{\mathcal{S}}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\hat {\boldsymbol{\mathrm{S}}} \\ $$$$\mathrm{Parametric}\:\mathrm{Surface} \\ $$$$\hat {\boldsymbol{\mathrm{S}}}\left({u},{v}\right)=\left(\mathrm{2}+\mathrm{sin}\left({u}\right)\right)\mathrm{cos}\left({v}\right)\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}}…

0-1-0-1-cos-max-x-3-y-3-2-dxdy-A-old-Quation-By-mr-univers-x-3-t-y-3-2-s-A-2-9-0-1-0-1-cos-max-t-s-t-2-3-s-1-3-dtds-0-1-0-1-cos-max-t-s-t-2-3-s-1-3-dt

Question Number 199638 by witcher3 last updated on 06/Nov/23 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{cos}\left(\mathrm{max}\left(\mathrm{x}^{\mathrm{3}} ,\mathrm{y}^{\frac{\mathrm{3}}{\mathrm{2}}} \right)\right)\mathrm{dxdy}=\mathrm{A} \\ $$$$\mathrm{old}\:\mathrm{Quation}\:\mathrm{By}\:\mathrm{mr},\mathrm{univers} \\ $$$$\mathrm{x}^{\mathrm{3}} =\mathrm{t},\mathrm{y}^{\frac{\mathrm{3}}{\mathrm{2}}} =\mathrm{s} \\ $$$$\mathrm{A}=\frac{\mathrm{2}}{\mathrm{9}}\int_{\mathrm{0}} ^{\mathrm{1}}…