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Vector Field / Integral

Posted on 2008-09-29
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Last Modified: 2008-10-15
A vector field is given as G = [25/(x^2 + y^2)](xa_x + ya_y), where a_x and a_y are unit vectors along the x and y axis respectively. Find the value of the double integral on the plane y = 7.

I'm a little confused as I have no limits of integration. I thought that if I possibly convert to cylindrical coordinates I might get a simpler version that would yield the limits of integration. However, I'm not entirely sure how I would convert this to cylindrical if necessary. I know x = r cos(phi), y = r sin(phi) and z = z, however, how do I convert the unit vectors?

Any help in the correct direction would be appricated.

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Question by:BrianGEFF719
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BigRat earned 250 total points
ID: 22604823
The function G tends to zero as the coordinates tend to infinity. The double integral will have a finite value.
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by:aburr
aburr earned 250 total points
ID: 22605028
I think the problem lacks a dfinition.  What double integral do you want?
 A line integral? (define the line)
A surface integral? (Define the surface)
A volume integral? Define the volume) (I know, you have a 2D problem here)
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by:BrianGEFF719
ID: 22606477
so integrate along x from -inf to inf and integrate along z from -inf to inf?
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by:BrianGEFF719
ID: 22606703
BigRat, how would I integrate this then?
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