- #1

Larrytsai

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## Homework Statement

Let C be the counter-clockwise planar circle with center at the origin and radius r > 0. Without computing them, determine F for the following vector fields whether the line integrals int(Fdr)

are positive negative or zero

F = xi + yj

F = -yi + xj

F = yi -xj

F= i + j

## The Attempt at a Solution

I applies greens theorem

for the first force vector F = xi + yj

so I take the partial of Q wrt x and get 1 and p wrt y and get 1

and i get double zero

but when i do this for 2nd one F = -yi + xj and 3rd one, my answers seem to be opposite of what i got.

F = -yi + xj

partial Q / partial x = -1

partial P/ partial y = 1

so i would get a negative number. but answer is positive.

greens theorem = double integral (-2)dA