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)=x2 i+xy jF(x,y) = x^2\ \mathbf{i} + xy\ \mathbf{j} along the quartile circle r(t)=cost i+sint jr(t) = \cos t\ \mathbf{i} + \sin t\ \mathbf{j} from t=0 t=0 to t=π2 t = \frac{ \pi}{2} ?

Details and assumptions

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

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