The problem of finding the work done in lifting a payload from the surface of the moon is another type of work problem. Suppose the moon has a radius of R miles and the payload weighs P pounds at the surface of the moon (at a distance of R miles from the center of the moon). When the payload is x miles from the center of the moon (x ≥ R), the force required to overcome the gravitational attraction between the moon and the payload is given by the following relation: required force = f(x) = R2P x2 pounds. How much work would be needed to raise the payload from the surface of the moon (i.e., x = R) to an altitude of 3R miles above the surface of the moon (i.e., x = 4R)?