Chapter 9, Problem 4P

A particle is accelerated along a curved path of length l under the action of an applied force $f\left(x\right)$, as shown in Fig. P9.4.

The total work done on the particle is

$W={\displaystyle \underset{0}{\overset{l}{\int }}f\left(x\right)dx}\text{ N-m}$

If $l=4.0\text{m}$, determine the work done for

(a) $f\left(x\right)=8x^3+6x^2+4x+2\text{N}$.

(b) $f\left(x\right)=4e^{-2x}\text{N}$ (c) $f\left(x\right)=1-2{\sin }^2\left(\frac{\pi x}{2}\right)\text{N}$ Hint: Use a trigonometric identity.