$2.$ Compute the work done by $\backslash (\backslash$mathbf$\{$F$\}=\backslash$left$($x y$,$ x$^\{2\}\backslash$right$)\backslash )$ in moving the particle once anticlockwise around the curve $\backslash ($ C $\backslash ),$ which is the boundary of the region in the first quadrant enclosed by the $\backslash ($ y $\backslash )-$axis, the line $\backslash ($ y$=$x $\backslash ),$ and the line $\backslash ($ y$=2-$x $\backslash ).$ Sketch the region. Use Green's Theorem to convert the line integral into a double integral, then evaluate the double integral.