Calculus 3: Line Integrals (28 of 44) Vector Field: Evaluate a Line Integral

In this video I will evaluate the line integral of (F)(dr) of a vector field f=(xy^2)i+(2)j+(x)k along a given path C.

Next video in the series can be seen at:

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So do the quantities given by all three methods represent the same thing? I know the F·dr method gives the work, but what exactly do the vectors represent from the previous 2 methods? Thanks Mr. van Biezen