What is the amount of work done by the particle moving in the force field \(F(x,y) = x^2\ \mathbf{i} + xy\ \mathbf{j}\) along the quartile circle \(r(t) = \cos t\ \mathbf{i} + \sin t\ \mathbf{j}\) from \( t=0 \) to \( t = \frac{ \pi}{2} \)?

**Details and assumptions**

Work done can be calculated using the formula \( W = \int_C F\cdot dr\).

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