What is the work done if \(\vec{F}=x y \hat{i}-y^{2} \hat{j}\) and \(\overrightarrow{d r}=\hat{i} d x+\hat{j} d y\) assuming the path is:

(a) a straight line where \(y=\frac{1}{2} x\) from \(A=(0,0)\) to \(B=(2,1)\) ?

(b) parabolic where \(y=\frac{1}{4} x^{2}\) from \(A=(0,0)\) to \(B=(2,1)\) ?

(c) Comment if the evaluated work is the same or different in (a) and (b).