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 22 hours ago
Mattos
2,73021321
asked 22 hours ago
Jackson Joffe
525
add a comment |
up vote
2
down vote
favorite
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 22 hours ago
Mattos
2,73021321
asked 22 hours ago
Jackson Joffe
525
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.
– Rafa Budría
12 hours ago
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
– Kuifje
12 hours ago
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
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 22 hours ago
Mattos
2,73021321
asked 22 hours ago
Jackson Joffe
525
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 22 hours ago
Mattos
2,73021321
asked 22 hours ago
Jackson Joffe
525
edited 22 hours ago
Mattos
2,73021321
asked 22 hours ago
Jackson Joffe
525
edited 22 hours ago
Mattos
2,73021321
edited 22 hours ago
Mattos
2,73021321
edited 22 hours ago
Mattos
2,73021321
2,73021321
asked 22 hours ago
Jackson Joffe
525
asked 22 hours ago
Jackson Joffe
525
asked 22 hours ago
Jackson Joffe
525
525
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.
– Rafa Budría
12 hours ago
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
– Kuifje
12 hours ago
add a comment |
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.
– Rafa Budría
12 hours ago
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
– Kuifje
12 hours ago
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.
– Rafa Budría
12 hours ago
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.
– Rafa Budría
12 hours ago
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
– Kuifje
12 hours ago
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
– Kuifje
12 hours ago
add a comment |
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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.
– Rafa Budría
12 hours ago
Are you sure it is not the flux of $curl vec {F} = (y,x^2,f(x,y,z))$ that you want to compute?
– Kuifje
12 hours ago