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I understand what line integral of a real function mean (the area) as well explained in https://www.physicsforums.com/showthread.php?t=115057

(Mentioning this link because there line integral of a real function has been explained.)

I was trying to understand what would the vector line integral graphically mean.

Like evaluate ∫F.dr where F is = x

^{2}i+xy j over c which is a square in the z plane bounded by lines x=0,x=a,y=0,y=a in the counterclockwise direction.

The result would be a

^{3}/2.

What would this mean graphically??

Please explain