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Find the work done by the force field $ \textbf{F} $ in moving an object from $ P $ to $ Q $.

$ \textbf{F}(x, y) = (2x + y) \, \textbf{i} + x \, \textbf{j} $; $ P(1, 1) $, $ Q(4, 3) $

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Vector Calculus

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Oregon State University

Harvey Mudd College

University of Nottingham

Boston College

so find the work done, moving from one point to another point without specifying the path. So the only way we can figure it all is if we can find the potential function. So we try to find this, and by definition, that gives us partial of partial tax. Should be this partial, have partial y should be that and that keeps us f equals X square process X y, plus any function off. Why the second equation gives us F because X Y process any function ofthe X because we're dealing Wisconsin off. When we are taking the directive with on ly one thereabout, then Kolinko Constant could be function off any other variables. So what we get is f equals a X squared plus X Y plus constant. And that means ah, that means work should be for four three minus F off one one Xs for y st sixteen plus twelve twenty eight f f c host one and white was wise one plus y goes to so we have twenty six us. Our final answer