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
multivariable-calculus divergence
edited Jan 9 at 18:52
caverac
14.6k31130
asked Jan 9 at 18:41
AlejandroAlejandro
1
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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
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$begingroup$
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
multivariable-calculus divergence
edited Jan 9 at 18:52
caverac
14.6k31130
asked Jan 9 at 18:41
AlejandroAlejandro
1
$endgroup$
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.
add a comment |
$begingroup$
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
multivariable-calculus divergence
edited Jan 9 at 18:52
caverac
14.6k31130
asked Jan 9 at 18:41
AlejandroAlejandro
1
$endgroup$
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
multivariable-calculus divergence
edited Jan 9 at 18:52
caverac
14.6k31130
asked Jan 9 at 18:41
AlejandroAlejandro
1
edited Jan 9 at 18:52
caverac
14.6k31130
asked Jan 9 at 18:41
AlejandroAlejandro
1
edited Jan 9 at 18:52
caverac
14.6k31130
edited Jan 9 at 18:52
caverac
14.6k31130
edited Jan 9 at 18:52
caverac
14.6k31130
14.6k31130
asked Jan 9 at 18:41
AlejandroAlejandro
1
asked Jan 9 at 18:41
AlejandroAlejandro
1
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.
add a comment |
add a comment |
1 Answer
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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.
answered Jan 9 at 18:57
Ted ShifrinTed Shifrin
64k44591
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Thanks for the reply. How do you identify how many surface it have? I'm still confused about simple solid regions.
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– Alejandro
Jan 10 at 3:03
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Start by drawing a sketch; your artwork needn't be perfect.
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– Ted Shifrin
Jan 10 at 3:37
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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.
answered Jan 9 at 18:57
Ted ShifrinTed Shifrin
64k44591
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
answered Jan 9 at 18:57
Ted ShifrinTed Shifrin
64k44591
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
answered Jan 9 at 18:57
Ted ShifrinTed Shifrin
64k44591
$endgroup$
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.
answered Jan 9 at 18:57
Ted ShifrinTed Shifrin
64k44591
answered Jan 9 at 18:57
Ted ShifrinTed Shifrin
64k44591
answered Jan 9 at 18:57
Ted ShifrinTed Shifrin
64k44591
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
add a comment |
$begingroup$
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
add a comment |
