Frightening Stokes Theorem Computation
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I came across a rather frightening problem in my problem set and I am confused about it.
I need to compute the flux of a field $vec F = langle y, x^2, z(x^2-y^3)^7 cos(e^{xyz}) rangle$ through the upward-pointing surface $z= sqrt {1 - frac {x^2} 9 - frac {y^2} 4} $.
I'm told it would be wise to use Stokes's Theorem and I'm also told to figure out the boundary to get a head start. I attempted to compute this integral with brute force, but it seems to be unintegrable that way.
How should I approach this problem?
calculus integration multivariable-calculus vector-fields stokes-theorem
edited Nov 30 '18 at 4:09
Mattos
2,73921321
asked Nov 30 '18 at 4:02
Jackson JoffeJackson Joffe
575
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add a comment |
$begingroup$
I came across a rather frightening problem in my problem set and I am confused about it.
I need to compute the flux of a field $vec F = langle y, x^2, z(x^2-y^3)^7 cos(e^{xyz}) rangle$ through the upward-pointing surface $z= sqrt {1 - frac {x^2} 9 - frac {y^2} 4} $.
I'm told it would be wise to use Stokes's Theorem and I'm also told to figure out the boundary to get a head start. I attempted to compute this integral with brute force, but it seems to be unintegrable that way.
How should I approach this problem?
calculus integration multivariable-calculus vector-fields stokes-theorem
edited Nov 30 '18 at 4:09
Mattos
2,73921321
asked Nov 30 '18 at 4:02
Jackson JoffeJackson Joffe
575
$endgroup$
$begingroup$
The boundary is not difficult to find, it's an ellipse of semi axis, 3 and 2. But the field is not the curl of anything. By other side, I don't see the problem easier using the divergence theorem.
$endgroup$
– Rafa Budría
Nov 30 '18 at 13:18
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Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
$endgroup$
– Kuifje
Nov 30 '18 at 13:45
add a comment |
$begingroup$
I came across a rather frightening problem in my problem set and I am confused about it.
I need to compute the flux of a field $vec F = langle y, x^2, z(x^2-y^3)^7 cos(e^{xyz}) rangle$ through the upward-pointing surface $z= sqrt {1 - frac {x^2} 9 - frac {y^2} 4} $.
I'm told it would be wise to use Stokes's Theorem and I'm also told to figure out the boundary to get a head start. I attempted to compute this integral with brute force, but it seems to be unintegrable that way.
How should I approach this problem?
calculus integration multivariable-calculus vector-fields stokes-theorem
edited Nov 30 '18 at 4:09
Mattos
2,73921321
asked Nov 30 '18 at 4:02
Jackson JoffeJackson Joffe
575
$endgroup$
I came across a rather frightening problem in my problem set and I am confused about it.
I need to compute the flux of a field $vec F = langle y, x^2, z(x^2-y^3)^7 cos(e^{xyz}) rangle$ through the upward-pointing surface $z= sqrt {1 - frac {x^2} 9 - frac {y^2} 4} $.
I'm told it would be wise to use Stokes's Theorem and I'm also told to figure out the boundary to get a head start. I attempted to compute this integral with brute force, but it seems to be unintegrable that way.
How should I approach this problem?
calculus integration multivariable-calculus vector-fields stokes-theorem
calculus integration multivariable-calculus vector-fields stokes-theorem
edited Nov 30 '18 at 4:09
Mattos
2,73921321
asked Nov 30 '18 at 4:02
Jackson JoffeJackson Joffe
575
edited Nov 30 '18 at 4:09
Mattos
2,73921321
asked Nov 30 '18 at 4:02
Jackson JoffeJackson Joffe
575
edited Nov 30 '18 at 4:09
Mattos
2,73921321
edited Nov 30 '18 at 4:09
Mattos
2,73921321
edited Nov 30 '18 at 4:09
Mattos
2,73921321
2,73921321
asked Nov 30 '18 at 4:02
Jackson JoffeJackson Joffe
575
asked Nov 30 '18 at 4:02
Jackson JoffeJackson Joffe
575
asked Nov 30 '18 at 4:02
Jackson JoffeJackson Joffe
575
575
$begingroup$
The boundary is not difficult to find, it's an ellipse of semi axis, 3 and 2. But the field is not the curl of anything. By other side, I don't see the problem easier using the divergence theorem.
$endgroup$
– Rafa Budría
Nov 30 '18 at 13:18
$begingroup$
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
$endgroup$
– Kuifje
Nov 30 '18 at 13:45
add a comment |
$begingroup$
The boundary is not difficult to find, it's an ellipse of semi axis, 3 and 2. But the field is not the curl of anything. By other side, I don't see the problem easier using the divergence theorem.
$endgroup$
– Rafa Budría
Nov 30 '18 at 13:18
$begingroup$
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
$endgroup$
– Kuifje
Nov 30 '18 at 13:45
$begingroup$
The boundary is not difficult to find, it's an ellipse of semi axis, 3 and 2. But the field is not the curl of anything. By other side, I don't see the problem easier using the divergence theorem.
$endgroup$
– Rafa Budría
Nov 30 '18 at 13:18
$begingroup$
The boundary is not difficult to find, it's an ellipse of semi axis, 3 and 2. But the field is not the curl of anything. By other side, I don't see the problem easier using the divergence theorem.
$endgroup$
– Rafa Budría
Nov 30 '18 at 13:18
$begingroup$
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
$endgroup$
– Kuifje
Nov 30 '18 at 13:45
$begingroup$
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
$endgroup$
– Kuifje
Nov 30 '18 at 13:45
add a comment |
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$begingroup$
The boundary is not difficult to find, it's an ellipse of semi axis, 3 and 2. But the field is not the curl of anything. By other side, I don't see the problem easier using the divergence theorem.
$endgroup$
– Rafa Budría
Nov 30 '18 at 13:18
$begingroup$
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
$endgroup$
– Kuifje
Nov 30 '18 at 13:45