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Help me figure out the average of a vector field

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savedadogs

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I have a vector function defined in the x-y plane which I would like to figure out the average. The function is

[A+A*B*cos(x-y)]X+[B+A*B*cos(x-y)]Y

where X and Y are the x-directed unit vector and y-directed unit vector respectively. I do not know how to approach this, should I solve it numerically or analytically? It seems like I should integrate the function over the plane of interest.
 

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