Chapter 6: Applications of Definite Integrals - Section 6.5 - Work and Fluid Forces - Exercises 6.5 - Page 348: 8

$1944 ft-lb$

Hooke's Law states that $F=k x$ Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$ This implies that $W=\int_0^{(18)} (144-4x) dx$ or, $W=[ 144x-4(\dfrac{x^2}{2})]_0^{(18)}=(144)(18-0)-2(18^2-0)$ Thus, $W=1944 ft-lb$