Many engineering problems involve the calculation of work. The general formula is Work = force * distance. Suppose that the force varies with distance. In such cases, the work equation is re-expressed as ∫Fdx, where W = work, J, xo and xn = the initial and final positions, respectively. Fx is a force that varies as a function of position, given by Fx = 0.80 - 0.125x - 0.009x^2 + 0.0002x^3. Determine the work done: a) analytically, b) using Simpson's 1/3 Rule, and c) using 3 segments of the Trapezoidal Rule. Compare (b) and (c) with (a).