Flux. Multivariable Calculus [closed]












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Find the flux of $F(x, y, z) = langle-x, -y, z^3rangle$ through the surface $S$ when $S$ is the part of the cone



$$z =sqrt{x^2 + y^2}$$



that lies between the planes $z = 1$ and $z = 3$, oriented upwards.




  • If I use the usual method, Im getting $1712pi/15$

  • If I use divergence theorem, Im getting $1916pi/15$


Is the divergence theorem not valid in here? thanks










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closed as off-topic by Adrian Keister, Eevee Trainer, Leucippus, Lord Shark the Unknown, max_zorn Jan 10 at 6:01


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Adrian Keister, Eevee Trainer, Leucippus, Lord Shark the Unknown, max_zorn

If this question can be reworded to fit the rules in the help center, please edit the question.





















    0












    $begingroup$


    Find the flux of $F(x, y, z) = langle-x, -y, z^3rangle$ through the surface $S$ when $S$ is the part of the cone



    $$z =sqrt{x^2 + y^2}$$



    that lies between the planes $z = 1$ and $z = 3$, oriented upwards.




    • If I use the usual method, Im getting $1712pi/15$

    • If I use divergence theorem, Im getting $1916pi/15$


    Is the divergence theorem not valid in here? thanks










    share|cite|improve this question











    $endgroup$



    closed as off-topic by Adrian Keister, Eevee Trainer, Leucippus, Lord Shark the Unknown, max_zorn Jan 10 at 6:01


    This question appears to be off-topic. The users who voted to close gave this specific reason:


    • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Adrian Keister, Eevee Trainer, Leucippus, Lord Shark the Unknown, max_zorn

    If this question can be reworded to fit the rules in the help center, please edit the question.



















      0












      0








      0





      $begingroup$


      Find the flux of $F(x, y, z) = langle-x, -y, z^3rangle$ through the surface $S$ when $S$ is the part of the cone



      $$z =sqrt{x^2 + y^2}$$



      that lies between the planes $z = 1$ and $z = 3$, oriented upwards.




      • If I use the usual method, Im getting $1712pi/15$

      • If I use divergence theorem, Im getting $1916pi/15$


      Is the divergence theorem not valid in here? thanks










      share|cite|improve this question











      $endgroup$




      Find the flux of $F(x, y, z) = langle-x, -y, z^3rangle$ through the surface $S$ when $S$ is the part of the cone



      $$z =sqrt{x^2 + y^2}$$



      that lies between the planes $z = 1$ and $z = 3$, oriented upwards.




      • If I use the usual method, Im getting $1712pi/15$

      • If I use divergence theorem, Im getting $1916pi/15$


      Is the divergence theorem not valid in here? thanks







      multivariable-calculus divergence






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      edited Jan 9 at 18:52









      caverac

      14.6k31130




      14.6k31130










      asked Jan 9 at 18:41









      AlejandroAlejandro

      1




      1




      closed as off-topic by Adrian Keister, Eevee Trainer, Leucippus, Lord Shark the Unknown, max_zorn Jan 10 at 6:01


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Adrian Keister, Eevee Trainer, Leucippus, Lord Shark the Unknown, max_zorn

      If this question can be reworded to fit the rules in the help center, please edit the question.







      closed as off-topic by Adrian Keister, Eevee Trainer, Leucippus, Lord Shark the Unknown, max_zorn Jan 10 at 6:01


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Adrian Keister, Eevee Trainer, Leucippus, Lord Shark the Unknown, max_zorn

      If this question can be reworded to fit the rules in the help center, please edit the question.






















          1 Answer
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          $begingroup$

          Sure, the divergence theorem is valid. But you're applying it to a region whose boundary consists of not only that surface $S$, but also two disks: $Sigma_1 = {x^2+y^2le 1, z=1}$ and $Sigma_2 = {x^2+y^2le 3, z=3}$. In addition, be careful with the orientations on those disks.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thanks for the reply. How do you identify how many surface it have? I'm still confused about simple solid regions.
            $endgroup$
            – Alejandro
            Jan 10 at 3:03












          • $begingroup$
            Start by drawing a sketch; your artwork needn't be perfect.
            $endgroup$
            – Ted Shifrin
            Jan 10 at 3:37


















          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          2












          $begingroup$

          Sure, the divergence theorem is valid. But you're applying it to a region whose boundary consists of not only that surface $S$, but also two disks: $Sigma_1 = {x^2+y^2le 1, z=1}$ and $Sigma_2 = {x^2+y^2le 3, z=3}$. In addition, be careful with the orientations on those disks.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thanks for the reply. How do you identify how many surface it have? I'm still confused about simple solid regions.
            $endgroup$
            – Alejandro
            Jan 10 at 3:03












          • $begingroup$
            Start by drawing a sketch; your artwork needn't be perfect.
            $endgroup$
            – Ted Shifrin
            Jan 10 at 3:37
















          2












          $begingroup$

          Sure, the divergence theorem is valid. But you're applying it to a region whose boundary consists of not only that surface $S$, but also two disks: $Sigma_1 = {x^2+y^2le 1, z=1}$ and $Sigma_2 = {x^2+y^2le 3, z=3}$. In addition, be careful with the orientations on those disks.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thanks for the reply. How do you identify how many surface it have? I'm still confused about simple solid regions.
            $endgroup$
            – Alejandro
            Jan 10 at 3:03












          • $begingroup$
            Start by drawing a sketch; your artwork needn't be perfect.
            $endgroup$
            – Ted Shifrin
            Jan 10 at 3:37














          2












          2








          2





          $begingroup$

          Sure, the divergence theorem is valid. But you're applying it to a region whose boundary consists of not only that surface $S$, but also two disks: $Sigma_1 = {x^2+y^2le 1, z=1}$ and $Sigma_2 = {x^2+y^2le 3, z=3}$. In addition, be careful with the orientations on those disks.






          share|cite|improve this answer









          $endgroup$



          Sure, the divergence theorem is valid. But you're applying it to a region whose boundary consists of not only that surface $S$, but also two disks: $Sigma_1 = {x^2+y^2le 1, z=1}$ and $Sigma_2 = {x^2+y^2le 3, z=3}$. In addition, be careful with the orientations on those disks.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 9 at 18:57









          Ted ShifrinTed Shifrin

          64k44591




          64k44591












          • $begingroup$
            Thanks for the reply. How do you identify how many surface it have? I'm still confused about simple solid regions.
            $endgroup$
            – Alejandro
            Jan 10 at 3:03












          • $begingroup$
            Start by drawing a sketch; your artwork needn't be perfect.
            $endgroup$
            – Ted Shifrin
            Jan 10 at 3:37


















          • $begingroup$
            Thanks for the reply. How do you identify how many surface it have? I'm still confused about simple solid regions.
            $endgroup$
            – Alejandro
            Jan 10 at 3:03












          • $begingroup$
            Start by drawing a sketch; your artwork needn't be perfect.
            $endgroup$
            – Ted Shifrin
            Jan 10 at 3:37
















          $begingroup$
          Thanks for the reply. How do you identify how many surface it have? I'm still confused about simple solid regions.
          $endgroup$
          – Alejandro
          Jan 10 at 3:03






          $begingroup$
          Thanks for the reply. How do you identify how many surface it have? I'm still confused about simple solid regions.
          $endgroup$
          – Alejandro
          Jan 10 at 3:03














          $begingroup$
          Start by drawing a sketch; your artwork needn't be perfect.
          $endgroup$
          – Ted Shifrin
          Jan 10 at 3:37




          $begingroup$
          Start by drawing a sketch; your artwork needn't be perfect.
          $endgroup$
          – Ted Shifrin
          Jan 10 at 3:37



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