Menu Close

Category: Integration

R-cos-max-x-3-y-3-2-dx-dy-where-R-0-1-0-1-

Question Number 199377 by universe last updated on 02/Nov/23 $$\:\:\int\underset{\mathrm{R}} {\int}\mathrm{cos}\:\left(\mathrm{max}\left\{\mathrm{x}^{\mathrm{3}} ,\:\mathrm{y}^{\mathrm{3}/\mathrm{2}} \right\}\right)\mathrm{dx}\:\mathrm{dy}\:,\:\mathrm{where}\:\mathrm{R}\:=\:\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$ Answered by witcher3 last updated on 04/Nov/23 $$\mathrm{i}\:\mathrm{will}\:\mathrm{Try} \\ $$…

1-1-1-x-2-1-x-2-1-1-x-2-y-2-1-1-y-2-x-2-y-2-z-2-5-2-dx-dy-dz-is-

Question Number 199369 by universe last updated on 02/Nov/23 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \:\int_{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}} ^{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }} ^{\mathrm{1}+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} {dx}\:{dy}\:{dz}\:\:{is}…

Question-199213

Question Number 199213 by emilagazade last updated on 29/Oct/23 Answered by witcher3 last updated on 29/Oct/23 $$\int_{\mathrm{a}} ^{\mathrm{b}} \left(\mathrm{x}−\left[\mathrm{x}\right]−\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{dx} \\ $$$$=\underset{\mathrm{k}=\mathrm{a}} {\overset{\mathrm{b}−\mathrm{1}} {\sum}}\int_{\mathrm{k}} ^{\mathrm{k}+\mathrm{1}} \left(\mathrm{x}−\left[\mathrm{x}\right]−\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{f}'\left(\mathrm{x}\right)\mathrm{dx}…

1-3-x-2-x-2-4x-dx-

Question Number 198948 by ArifinTanjung last updated on 26/Oct/23 $$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −\mathrm{4x}}\:\mathrm{dx}=\:…. \\ $$ Answered by ajfour last updated on 26/Oct/23 $${I}=\frac{\mathrm{1}}{\mathrm{2}}\int_{−\mathrm{1}} ^{\:\mathrm{1}} \frac{\mathrm{2}{tdt}}{{t}^{\mathrm{2}}…

radius-r-circle-x-2-y-2-z-2-r-2-F-x-y-z-yze-1-xe-2-xye-3-Find-flux-F-n-dS-

Question Number 198802 by MathedUp last updated on 24/Oct/23 $$\mathrm{radius}\:{r}\:\mathrm{circle}\:;\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\hat {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)={yz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +{x}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xy}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\mathrm{Find}\:\mathrm{flux}\:\boldsymbol{\rho}=\int\int_{\:\boldsymbol{\Sigma}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\hat…