Work Done by Force Field (Part 2)

A particle in the $xy$ -plane is acted upon by a force field described by the equation below: $\large{\vec{F} = x \hat{\imath} + y \hat{\jmath}}.$ How much work does the force field do on the particle if the particle makes one complete revolution over a unit circle centered on the origin?

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Notes:

• $\hat{\imath}$ and $\hat{\jmath}$ denote unit vectors in the $x$ and $y$ directions, respectively.
• Give your answer to 3 decimal places.