- #1
advphys
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Hi to all,
Evaluate the surface integral of the vector F=xi+yj+zk over that portion of the surface x=xy+1
which covers the square 0≤x≤1 , 0≤y≤1 in the xy plane
∫∫F.ndσ
n=∇g/|∇g|
maybe transformation to the volume integral
g(x,y,z)=xy+1-z
n=∇g/|∇g|=(yi+xj-k)/√(y2+x2+1)
Plugging into integral,
i finally got
∫∫((xy-1)/(√(y2+x2+1))) dxdy
both x and y are from 0 to 1.
But i could not take this integral without help of a computer.
Since this is from a book's ordinary question i don't think it needs such a treatment.
I think i could transform the surface integral into a volume integral but there is not a well defined volume that can be used.
So, i stuck at this point.
Thanks.
Homework Statement
Evaluate the surface integral of the vector F=xi+yj+zk over that portion of the surface x=xy+1
which covers the square 0≤x≤1 , 0≤y≤1 in the xy plane
Homework Equations
∫∫F.ndσ
n=∇g/|∇g|
maybe transformation to the volume integral
The Attempt at a Solution
g(x,y,z)=xy+1-z
n=∇g/|∇g|=(yi+xj-k)/√(y2+x2+1)
Plugging into integral,
i finally got
∫∫((xy-1)/(√(y2+x2+1))) dxdy
both x and y are from 0 to 1.
But i could not take this integral without help of a computer.
Since this is from a book's ordinary question i don't think it needs such a treatment.
I think i could transform the surface integral into a volume integral but there is not a well defined volume that can be used.
So, i stuck at this point.
Thanks.