A cutting tool under microprocessor control has several forces acting on it$.$ One force is F$=$xy$2$j$^,$ a force in the negative y$-$direction whose magnitude depends on the position of the tool. The constant is $=2\mathrm{.}05$ N$/$m$3.$Consider the displacement of the tool from the origin to the point x$=3\mathrm{.}45$ m $,$ y$=3\mathrm{.}45$ m $.$ Calculate the work done on the tool by F$$ if this displacement is along the straight line y$=$x that connects these two points. Calculate the work done on the tool by F$$ if the tool is first moved out along the x$-$axis to the point x$=3\mathrm{.}45$ m $,$ y$=0$ and then moved parallel to the y$-$axis to x$=3\mathrm{.}45$ m $,$ y$=3\mathrm{.}45$ m $.$ Compare the work done by F$$ along these two paths. Is F$$ conservative or nonconservative?