$(12$ points$)$ In a two$-$dimensional world, suppose that the gravitational force between mass m and

mass M is given by

F$($x$,$y$)=(-$mMGx$)/(($x$^(2)+$y$^(2))^((3)/(2)))$i$+(-$mMGy$)/(($x$^(2)+$y$^(2))^((3)/(2)))$j

where G is a constant and mass M is fixed at the origin. Show that F is a conservative force field.

Use this fact to compute the work $\backslash$int$\_$C F$*$dr done by the force field in moving the mass m along a

smooth curve C from $(-3,4)$ to $(1,0).$