Chapter 4.6, Problem 41E

Work To determine the size of the motor required to operate a press, a company must know the amount of work done when the press moves an object linearly 5 feet. The variable force to move the object is

$F\left(x\right)=100x\sqrt{125-x^3}$

where F is given in pounds and x gives the position of the unit in feet. Use Simpson’s Rule with n = 12 to approximate the work W (in foot-pounds) done through one cycle when

$W={\displaystyle {\int }_0^{5}F\left(x\right)dx.}$