Word Count : 301

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To calculate the work done by the force \(\vec{F} = (x+y) \hat{i} + xy \hat{j}\) along the given circular path, we use the line integral: \[ W = \int_C \vec{F} \cdot d\vec{r} \] ### Step 1: Parameterizing the Path The given path is the circle: \[ x^2 + y^2 = 4 \] We use the parametric equations for a circle of radius 2: \[ x = 2\cos t, \quad y = 2\sin t, \quad t _______ ______ _______ ______ _____ __________ _________.
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