Lou's latest invention, aimed at urban dog owners, is the X-R-Leash. It is made of a rubber-like material that exerts a force F_x = −kx − ax² when it is stretched a distance x, where k and a are constants. The ad claims, "You'll never go back to your old dog leash after you've had the thrill of an X-R-Leash experience. And you'll see a new look of respect in the eyes of your proud pooch." Find the work done on a dog by the leash if the person remains stationary and the dog bounds off, stretching the X-R-Leash from x = 0 to x = x₀.