# May the force (field) be with you

Calculus Level 3

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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